Republicans in the US Senate are asking Democrats to delay the start of former President Donald Trump's impeachment trial until February.
They argue this will give Mr Trump time to prepare a defence. He is accused of inciting insurrection after supporters of his stormed the Capitol this month.
House of Representatives' Democrats are ready to hand the charge to the Senate.
Mr Trump flew to Florida as his term ended on Wednesday, skipping his successor Joe Biden's inauguration.
On 6 January, the then president told protesters near the White House to "peacefully and patriotically" make their voices heard as they prepared to march towards the US Capitol building. He also told them to "fight like hell".
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The demonstration turned ugly as a mob forced its way into the congressional complex where lawmakers were certifying Mr Biden's election victory.
Four protesters and a Capitol Police officer died in the mayhem.
A week later, Mr Trump became the first US president to be impeached twice. His trial in the Senate will be the only one ever to have taken place after a president has left office.
Impeachment: The basics
What is impeachment? Impeachment is when a sitting president is charged with crimes. In this case, former President Trump is accused of having incited insurrection
What has already happened? The House of Representatives voted to impeach Mr Trump for a second time on 13 January, shifting the process to the Senate for a trial - but that trial could not be carried out before he left office on 20 January
So what does it mean? A trial can still happen although Mr Trump's term has ended, and senators can vote to bar him from holding public office again
What are Republicans asking for?
On a call to his fellow Republican senators on Thursday, Senate minority leader Mitch McConnell said he had asked House Democrats to hold off sending the single impeachment article to the Senate until 28 January - a move which would kick-start the trial's first phase.
Under this timetable, Mr Trump would then have two weeks - until 11 February - to submit his pre-trial defence. Arguments would be expected to begin in mid-February.
Republicans, who as of Wednesday no longer control the Senate, need the new Democratic majority leader, Chuck Schumer, to agree to the idea.
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Mr McConnell said in a statement: "Senate Republicans are strongly united behind the principle that the institution of the Senate, the office of the presidency, and former President Trump himself all deserve a full and fair process that respects his rights and the serious factual, legal, and constitutional questions at stake."
Senator John Cornyn of Texas told Reuters news agency that he and fellow Republicans had been discussing the need to allow Mr Trump "due process".
Ten Republicans sided with House Democrats in impeaching the outgoing president on 14 January.
Even though Democrats now narrowly control the Senate, they would need the support of at least 17 Republicans in order to convict Mr Trump, because a two-thirds vote is required.
A handful of Senate Republicans have indicated they are open to conviction, but most have either cast doubt on the legality of trying a president after he has left office, or said the process would be too divisive.
Will Democrats go along with this schedule?
Mr Schumer's office has not yet released a statement on Mr McConnell's proposal.
House Speaker Nancy Pelosi declined to answer journalists' questions on Thursday about when she would submit the charge.
But she said Mr Trump did not deserve a "get out of jail card" just because he had left office.
Senator Chris Coons said fellow Democrats might be receptive to a delay in the impeachment trial if Republicans helped push through Mr Biden's cabinet nominees.
"If not," the Delaware senator told CNN, "you'll quickly find Democrats frustrated and insisting that we move ahead with the accountability that could be delivered by an impeachment trial."
A dilemma for Democrats
Mitch McConnell's proposal to delay Donald Trump's Senate impeachment trial seems destined to split the Democrats. And that's probably exactly why the wily Senate minority leader suggested it.
Some on the left will welcome a two-week postponement, as it will give the Senate time to confirm presidential appointments and begin work on their legislative agenda. Before his inauguration, Joe Biden expressed concern about being unable to quickly staff his administration and recommended the Senate try to conduct a part-time trial while doing other business.
Other Democrats prefer a speedy trial. They believe that delays will reduce the pressure on Republicans to vote to convict, as the violence of 6 January recedes from memory. The sooner Mr Trump is held accountable for his actions, in their mind, the better.
Mr McConnell's move is also a bid to steal the initiative from the Democrats. At the moment, according to Senate rules, a trial has to commence as soon as House Speaker Pelosi transmits the articles of impeachment to the Senate. She's the only one who can light the fuse on this political bomb.
Even though Mr McConnell no longer runs the Senate, he's showing he still has some tricks up his sleeve.
Where is Trump now?
Donald Trump left the White House on Wednesday morning and flew on Air Force One to his golf club in Palm Beach, Florida.
His motorcade passed hundreds of well-wishers before he arrived at Mar-a-Lago minutes before Mr Biden took the oath of office in Washington DC just before noon.
Mr Trump is expected to live at the resort he calls his "Winter White House", despite concerns from some neighbours about the increased traffic and heightened security an ex-president would bring to their doorstep.
He is planning to maintain a tight-knit coterie of former White House aides in Florida.
According to reports, he wants to raise $2bn (£1.46bn) for his presidential library and has floated the idea of forming a new political party called the Patriot Party.
Who will defend Trump?
Mr Trump has hired South Carolina-based lawyer Butch Bowers to represent him in his Senate impeachment trial, according to Senator Lindsey Graham.
According to his website, Mr Bowers was a special counsel on voting matters at the US Department of Justice under President George W Bush.
He also served as counsel to two former governors of South Carolina, Nikki Haley and Mark Sanford.