Donald Trump was forced to pause his UN speech amid laughter at claims he has "accomplished almost more than any administration in the history of our country".
In an almost 40-minute address to the assembled United Nations General Assembly members in New York, he reserved his most stinging remarks for Iran, who he described as the "world's leading sponsor of terrorism".
He also praised his team in Washington for its work surrounding the denuclearisation of the Korean Peninsula and touched on some of the world's most devastating conflicts, including Syria, Iraq, Yemen and Venezuela.
Opening his speech, he said: "One year ago I stood before you at this grand hall. I addressed the threats facing our world and presented a vision for a brighter future.
"Today, I stand before the United Nations to share the extraordinary progress we've made.
"In less than two years, my administration has accomplished almost more than any administration in the history of our country."
Laughter and applause filled the room, forcing the President to pause, before continuing: "America...it's so true...I didn't expect that reaction, but OK."
Ahead of his address to the United Nations General Assembly, President Donald Trump has said he had no plans to meet with Iranian leader Hassan Rouhani at the gathering of world leaders "despite requests" to do so.
Trump doubles down on messages from 12 months ago
Trump has just wrapped up a 35-minute speech that was, well, very Trumpian, writes Harriet Alexander.
There were no real surprises - although he was somewhat taken aback by the laughter that greeted his claim to have achieved more than any other administration - and it followed the pattern set last year.
There was the recap of domestic success, the celebration of his North Korea tactics, and the defence of some of his more controversial decisions - reducing the refugee numbers to 30,000; withdrawing from the UN human rights council; pulling out of the Iran nuclear deal.
Of course, Iran came in for the strongest attack - he described the country as the world's biggest sponsor of terrorism, and called on other nations to back their economic warfare against Tehran.
Venezuela and Cuba also came in for a predictable kicking.
In essence, he was doubling down on the previous 12 months, in an unapologetic fashion. He did, however, manage to stick to the script, avoid rambling, and keep his cool.
His team will be pleased with that performance.
'Let us choose a future of patriotism'
Closing his speech, Mr Trump said: "In America we believe in the majesty of freedom, self-government and the rule of law.
"A culture build on strong families, deep faith and fierce independence. "e celebrate our heroes and above all we love our country
"Inside this great chamber and in all those listening around the globe, there is the heart of a patriot that feels the same powerful love to your nation, the same intense loyalty to your homelands.
"It has inspired reform and revolution, sacrifice and selflessness, scientific breakthroughs and magnificent works of art.
"Our task is not to erase it, but to embrace it, to build with it, to draw on its ancient wisdom, and to find within it a way to make out nations greater and the world better.
"Together let us choose a future of patriotism
"Forever strong, forever sovereign, forever just and forever thankful for the grace and the goodness and the glory of God.
"Thank you, God bless you and God bless the nations of the world."
Trump to the world - 'Make your countries great again'
Having earlier talked about the ongoing building of the wall on the Mexican-US border, Mr Trump told the room that illegal immigration was behind the "flow of deadly drugs" in America.
"It hurts hard-working citizens and has produced a vicious cycle of crime and poverty. Only by destroying criminal gangs can we establish a real foundation for prosperity."
The President called for every country to be in control of their own migration policies, stating that he respects each nation's decisions, "just as we ask every country to respect ours, which we are doing".
"Migration should not be governed by a national body which is unccountable by our own citizens.
"Make their countries great again."
Most stinging criticism reserved for Iran
As expected, the strongest words have come so far on Iran, writes Harriet Alexander.
Trump last year at this podium said the Iran nuclear deal was an embarrassment, adding: "The Iranian government masks a corrupt dictatorship behind the false guise of a democracy. It has turned a wealthy country with a rich history and culture into an economically depleted rogue state whose chief exports are violence, bloodshed, and chaos. The longest-suffering victims of Iran's leaders are, in fact, its own people."
This year, it's more of the same - calling Iran the world's largest supporter of terrorism, and demanding that other nations back the US in its economic warfare.
Tomorrow Trump holds a UN Security Council meeting on Iran; definitely one to watch.
The ICC has 'no authority' in America, Trump says
"America will always act in my country's interest," Trump said.
He accused the International Criminal Court of "shielding human rights abusers while bashing the US".
"As far as America is concerned, the ICC has no authority. We will never surrender America to unelected," he said.
"America is governed by Americans," adding that he rejects globalism.
Measured address so far from Trump
So far, so measured from Trump, writes Harriet Alexander.
He's opened with a defence of his domestic policies - unusual, but not for him - and then gone on to talk about his successes in North Korea, progress in the Middle East, and policy on refugees.
This is interesting; at the end of August the Trump administration announced it was ending financial backing for the UN refugee body supporting Palestinians, and on September 17 the US dismayed many by announcing it was slashing, once again, the number of refugees admitted.
In the 2018-19 fiscal year, beginning on Oct 1, only 30,000 refugees will be allowed.
This is down from 45,000 last year - already a historic low.
Under George W Bush, even after 9/11, 70,000 were permitted. And only 60 Syrian refugees have been allowed into the US this year.
He's defending that policy here, saying it's the best option for the refugees, and the best use of finite resources.
Iran is 'world's leading sponsor of terrorism', Trump says
Mr Trump said: "The Iran deal was a windfall for Iran's leaders. In the years since the deal was reached, Iran's military budget increased by 40%."
The President said the money was used to finance terrorism and "fund havoc and slaughter in Syria and Yemen".
"The US has launched a campaign of economic pressure to deny the regime the funds to its pursue its agenda. Additional sanctions will resume, and war will follow.
"We cannot allow the world's leading sponsor of terrorism to possess the means to deliver a nuclear warhead to any city on earth.
"We ask all nations to isolate Iran's regime as long as its aggression continues."
Trump moves on to Syria
"The ongoing tragedy in Syria is hearbreaking," the President said.
He said that "bloodthirsty" Isil had been flushed out of their territories in Iraq and Syria.
Mr Trump added: "I commend the people of Jordan and other neitghbouing countreis for hosting refusges from this very brutal civil war."
US 'will not tell you how to live, work or worship'
The US President continued: "The US will not tell you how to live or work or worship. We only ask that you honor our sovereignty in return.
"It has been my honour to represent the US abroad. Our approach has always yielded change.
"We have engaged with North Korea with a bold and new approach to peace.
"The missiles and rockets are no longer flying in every direction.
"I would like to thank Chairman Kim for his courage and the steps he has taken."
Trump opens with his administration's success
Once again, Trump opens by trumpeting his own success, writes Harriet Alexander.
This is pretty unusual at this international forum - indeed, when he did it last year, everyone was taken aback.
But, of course, Trump writes his own rules.
He plays, as ever, to his base: the stock market, border wall and military are all emphasised.
We knew this was coming - he has been tweeting, in the run up, about how he was looking forward to talking about US triumphs, with him at the helm.
Laughter from leaders causes Trump to pause speech
"One year ago is stood before you at this grand hall.
"I addressed the threats facing our world and presented a vision for a brighter future.
"Today I stand before the United Nations to share the extraordinary progress we've made.
"In less than two years, my administration has accomplished almost more than any administration in the history of our country."
Laughter and applause fills the room, forcing the President to pause, before continuing: "America...it's so true...I didn't expect that reaction, but OK."
Trump takes to the stage
After the Ecuadorian leader took his place, the US President is now up.
Trump won't meet Iran until "they change their tune"
President Donald Trump says he won't meet with Iran's leadership "until they change their tune."
Questioned as he arrived late at United Nations headquarters Tuesday, Trump said Iran has acted "very badly." He says the US is doing "many things" right now with respect to Iran, including sanctions.
Trump earlier this year withdrew the U.S. from a nuclear agreement between Iran and world powers and reinstated economic sanctions.
Trump says he looks forward to having a "great relationship" with Iran but "Iran has to change its tune."
While Trump spoke in sour terms about current relations with Iran, he spoke glowingly of his budding friendship with North Korean leader Kim Jong-un.
Trump and Kim met in June in Singapore. Trump says, "We're doing very well with North Korea."
Trump arrives late with Melania and Ivanka
It's 10.15am in New York, and Trump is only just arriving at the UN now, writes Harriet Alexander.
You would have imagined he'd be here a good half an hour ago.
He's accompanied by his wife, Melania, daughter Ivanka, and Nikki Haley, the US ambassador to the UN.
We can only speculate as to why he's running late - last minute speech changes, perhaps?
Confusion over Trump's absence
Donald Trump was scheduled to speak second at the podium, but the Ecuadorian leader Lenin Moreno Garcés is on stage.
From New York, Harriet Alexander reports:
In a surprising turn of event, Donald Trump is not speaking second, as advertised. The president of Ecuador is going next.
Why is Trump late?
This is really strange.
The White House press pool reported half an hour ago, at 9:27am local time, that they were still at the hotel. I wonder what is going on?
Brazilian President talks of human rights struggles
María Fernanda Espinosa, President of the United Nations General Assembly, greeted the gathered leaders with her welcoming speech, before inviting Michel Temer to the podium.
The Brazilian President talked of his country's resilience in the face of the world's challenges, specifically mentioning human rights.
Trust at breaking point amid 'increasingly chaotic' world, Secretary-General says
United Nations Secretary-General Antonio Guterres warned leaders on Tuesday that world order is "increasingly chaotic," trust is at breaking point and shifts in the balance of power may increase the risk of confrontation, though he did not lay blame.
Talking to the 193-member UN General Assembly, he said that multilateralism is under fire when it is needed most.
Guterres said: "Individual leaders have the duty to advance the well-being of their people. But it runs deeper ... As guardians of the common good, we also have a duty to promote and support a reformed, reinvigorated and strengthened multilateral system."
He called for a renewed commitment to a rules-based order with the United Nations at its center and warned against a spreading "politics of pessimism."
"Those who see their neighbors as dangerous may cause a threat where there was none. Those who close their borders to regular migration only fuel the work of traffickers," Guterres said.
"And those who ignore human rights in combating terrorism tend to breed the very extremism they are trying to end."
He also urged leaders to tackle climate change with a greater sense of ambition and urgency and said he would hold a summit on the issue in September next year.
The Trump administration withdrew from a global accord to reduce emissions last year.
"If we do not change course in the next two years, we risk runaway climate change," Guterres said.
The General Assembly schedule
Donald Trump is the second country representative to speak today, as per tradition, writes Harriet Alexander.
The general assembly always opens with remarks by the Secretary-General, and then the president of the general assembly - this time, it's María Fernanda Espinosa Garcés, from Ecuador.
Then comes Brazil - a tradition dating back to 1955. According to the United Nations, during the organisation's early years no one ever wanted to be the first to speak, and Brazil always ended up volunteering to go first. The host country, which is the United States, always speaks second.
After that, it's a bit of a free-for-all - heads of state go first, and then prime ministers, followed by foreign ministers and more junior representatives. But there's always some jostling for priority; it's more prestigious to speak on the first day, in the morning, than later on in the week.
Here's who else is speaking today - France, Iran and Turkey being the obvious highlights of the morning session.
1. Secretary-General of the United Nations
2. President of the General Assembly
María Fernanda Espinosa Garcés
4. United States of America
Lenin Moreno Garcés
Recep Tayyip Erdoğan
Enrique Peña Nieto
Martin Vizcarra Cornejo
King Abdullah II ibn Al Hussein
Amir Tamim bin Hamad Al -Thani
Faure Essozimna Gnassingbé
18. South Africa
Matamela Cyril Ramaphosa
Arthur Peter Mutharika
Abdel Fattah al-Sisi
Mario Abdo Benitez
25. Sri Lanka
Edgar Chagwa Lungu
28. Democratic Republic of the Congo
Joseph Kabila Kabange
31. Bosnia and Herzegovina
Filipe Jacinto Nyusi
33. Marshall Islands
34. Dominican Republic
Danilo Medina Sánchez
Saad-Eddine El Othmani
Harriet Alexander, Telegraph's US Correspondent, live from New York
The Telegraph's US Correspondent Harriet Alexander is at the United Nations General Assembly - here is an update from a soggy Big Apple:
Good morning from a very rainy New York, where the skies are leaden and everyone is currently dodging umbrella spikes and wading through puddles to get inside the main UN complex.
Yet today is going to be a good day! Donald Trump is due to speak in around half an hour's time, and it's something you won't want to miss.
You can read below what to expect from his speech.
It's likely to be a good day for Trump - regardless of the outcry his speech provokes, he loves nothing more than a headline. It'll be a good day for Israel, as he will doubtless leap to their defence once again.
It'll be an interesting day for North Korea - expect a far more conciliatory tone than last year, where he mocked "rocket man" Kim Jong-un and threatened to "totally destroy" the country. But don't expect him to announce an easing of sanctions - something Pyongyang desperately wants.
And it'll be a bad day, for sure, for Iran - Trump is champing at the bit to have a go at them - probably Venezuela too.
It's also a pretty bad day for New Yorkers in general. The streets are totally gridlocked, traffic is diverted, and the already-stinky subway smells like a wet dog.
Trump to praise his own team
Expect Mr Trump to lavish praise on his own team, writes Harriet Alexander.
Mr Pompeo is visibly happier as secretary of state than his poor predecessor, Rex Tillerson. On Monday Mr Pompeo was beaming and jovial as he previewed the days ahead, telling the assembled crowd in a New York hotel that he was relishing what he termed "the Super Bowl of diplomacy".
"Americans can be proud of how our entire team is executing on the field today," said Mr Pompeo.
"Americans expect the United States to assert bold leadership on the world stage that reflects our values. And under President Trump, we are certainly leading from the front."
He is helped by the fact that he has been able to bring with him a slew of envoys, aides and diplomats - Mr Tillerson, by contrast, was proud to bring a skeleton staff, to save money.
Mr Pompeo has in recent weeks appointed a special envoy for Iran policy and another for North Korea nuclear talks, and also hired two to focus on Syria, and one for reconciliation in Afghanistan.
"What we will try to do is have all hands on deck," said Mrs Haley.
The US delegation this year includes Mr Pence, Steve Mnuchin, the treasury secretary, and Mr Trump's daughter Ivanka and her husband, Jared Kushner.
On Monday, Mr Pompeo was positively glowing at the thought of the week ahead.
The gathering, he concluded, would enable Mr Trump to deliver "a recap about how his call for every nation to do its part has paid dividends for the United States, and the world, over this past year."
Syria, Yemen and Venezuela
The US president will have little choice but to mention two of arguably the biggest crises in the world today - Syria and Yemen.
Yet don't expect any dramatic announcement, or change of policy.
The two conflicts are too intractable to shout about. And, given the involvement of Russia and Saudi Arabia respectively, too much of a hornets' nest to kick.
Mike Pence, the vice president, is hosting an event focusing on Venezuela during the week - and Mr Trump is likely to use his podium to berate the socialist regime in Caracas.
Last year, Mr Trump was brutal, describing the government of Nicolas Maduro as a "corrupt regime" which has "destroyed a prosperous nation by imposing a failed ideology that has produced poverty and misery everywhere it has been tried."
He added: "To make matters worse, Maduro has defied his own people, stealing power from their elected representatives to preserve his disastrous rule.
"The Venezuelan people are starving and their country is collapsing. Their democratic institutions are being destroyed. This situation is completely unacceptable and we cannot stand by and watch."
He is unlikely to have changed his tone. Cuba may well also come in for a kicking - despite this being the first general assembly since the Cuban Revolution without a Castro at the helm. Miguel Diaz-Canel, elected in April, is making his own UN debut.
North Korea - a year on
The most dramatic change in tone from last year's address will certainly come when Mr Trump moves to discuss North Korea.
Gone will be the insults and threats; in their place, expect to see warm words of encouragement for a man he now considers almost a friend.
"Chairman Kim has been really very open and terrific, frankly," said Mr Trump on Monday, adding that he hopes to meet him again soon.
Buoyed by the thrill of his historic June summit in Singapore - the first time the leaders of the US and North Korea had ever met - Mr Trump is keen to emphasise that he is making progress on the Korean peninsula, despite critics pointing out that little of note has actually been achieved.
His speech will doubtless recap the "triumph" of the meeting, and stress its unprecedented nature.
His assurance that "everybody can now feel much safer than the day I took office", because "there is no longer a Nuclear Threat from North Korea", saw eye rolls from experts, who pointed out that no actual steps had been taken to remove the threat.
But that doesn't mean Mr Trump won't repeat the assertion on Tuesday.
Trump to mount pressure on Iran
Mr Trump is also certain to return to the topic of Iran - especially given that it's his first UN speech since pulling the US out of the nuclear agreement, in May, writes Harriet Alexander.
"You can bet the president will have well-deserved strong words for the Iranian regime, which is among the worst of violators of UN Security Council resolutions, if not the absolute worst in the world," said Mr Pompeo on Monday.
"He'll call on every country to join our pressure campaign in order to thwart Iran's global torrent of destructive activity."
It's not a position that has received universal support in the US. Ahead of the general assembly, a bipartisan group of national security leaders, including Madeleine Albright, the former secretary of state, and James Clapper, the former director of national intelligence, strongly criticised Mr Trump's Iran strategy in a statement issued on Sunday.
"The Trump administration's Iran strategy is to assert maximum economic, political and military pressure to change Iran's behaviour and threaten, if not cause, collapse of the regime," they wrote.
"But since it has not undertaken diplomatic engagement on any of its twelve demands on Iran, the administration has left Iran the option of either capitulation or war."
Mr Trump will also likely preview the Security Council meeting that he is chairing on Wednesday morning - an eagerly-watched gathering, not least to see how the freewheeling president copes with hosting a tightly-scripted diplomatic dance.
Watch closely to see how Mr Trump describes that Security Council meeting.
His aides have been trying to explain that the meeting needs to be about a broad range of issues, including Iran: if it is just about Iran, the Iranian leader, Hassan Rouhani, can have a seat at the table - a scenario US diplomats are keen to avoid.
The state department has since been at pains to describe the meeting as being about non-proliferation of nuclear weapons, and instability in the Middle East in general.
On September 7, the US mission to the UN issued a statement saying the meeting would focus on a "broader range of issues," including the "proliferation of weapons of mass destruction" in addition to Iran's destabilising activities.
Yet on Friday, Mr Trump tweeted: "I will Chair the United Nations Security Council meeting on Iran next week!"
Furthermore, Theresa May, Emmanuel Macron and Sergey Lavrov, the Russian foreign minister, all plan to attend the meeting - meaning that fireworks could ensue if Mr Trump steers the meeting towards open condemnation of the nuclear deal. US diplomats are deeply worried about a possible confrontation with key allies.
"Trump risked a collision with the UK and France over Iran at the UN," said Richard Gowan, a senior fellow at the United Nations University, a global affairs think tank.
He told The Washington Post that Mrs May and Mr Macron "would have had no choice but to defend the nuclear deal in the council."
"I don't think anyone liked the idea of the president having to sit through stern defences of the Iran deal from May and Macron. He could have got very tetchy, as he did at Nato and the G-7, or walked out of the council causing a diplomatic fuss."
The US' domestic triumphs
Equally, Mr Trump is likely to use his speech once again to trumpet his own domestic policies.
Last year he surprised many by opening with a recap of his successes, boasting how well the US stock market was doing, and how the US unemployment rate was falling.
Expect more of the same.
His diehard supporters may not pay attention to what Mr Trump himself derided, as president-elect, as "just a club for people to get together, talk and have a good time" - but Mr Trump is never one to miss an opportunity to shout about his own successes.
"Our economy is the envy, right now, of the world," said Mr Trump on Monday, ahead of his talks with South Korean president Moon Jae-in.
"We are the fastest-growing economy in the world."
Since Mr Trump took office, the nation's gross domestic product has grown an average of 2.7 per cent per quarter, and unemployment is at a generational low. Business is booming, and the stock market is soaring. He will want everyone to know.
Trump will again put America first
Mr Trump's "America First" rhetoric raised eyebrows last year, with critics seeing it as a disturbingly isolationist and unilateral message - a sharp, deliberate contrast to the globalist view of Barack Obama.
"I will always put America first, just like you, as the leaders of your countries, will always, and should always, put your countries first," said Mr Trump.
It's a message he intends to hammer home again this year.
Mrs Haley noted, ahead of Tuesday's speech, that "he wants to talk about protecting US sovereignty."
She added: "It's not saying multilateralism can't work. It is saying sovereignty is a priority over all of that."
Mike Pompeo, the secretary of state, agreed, saying on Monday: "Whether it's security issues, economic issues, human rights, or anything else, the president is asking for countries to exert their sovereignty to solve challenges and listening to what America can do to help."
What to expect from Donald Trump's speech
When President Donald Trump made his United Nations debut a year ago, addressing the general assembly for the first time, he was determined to make waves, writes Harriet Alexander.
And, of course, he did.
The president, by then eight months into the role, launched into a hair-raising tirade that shook the usually-staid chamber.
He began by trumpeting his own domestic economic policies, before switching to give his take on world affairs.
Kim Jong-un was labelled a suicidal "rocket man", whose "depraved" country Mr Trump may decide to "totally destroy". The Iran nuclear deal was an "embarrassment".
On Tuesday Mr Trump is back, speaking shortly after 9am in what will, unsurprisingly, be one of the most closely-watched moments of the annual jamboree.
"Last year we started UNGA and it was trying to figure what the US presence was going to be," said Nikki Haley, the US ambassador to the UN, on Monday. "This year, we're here with a bang."