South Africa's health minister says there is "absolutely no need to panic" over the new coronavirus variant Omicron, despite a surge in cases.
"We have been here before," Joe Phaahla added, referring to the Beta variant detected in South Africa last December.
South Africa also condemned the travel bans imposed on the country, saying they should be lifted immediately.
Omicron has been classed as a "variant of concern". Early evidence suggests it has a heightened re-infection risk.
The heavily mutated variant was detected in South Africa earlier this month and then reported to the World Health Organization (WHO) last Wednesday.
The variant is responsible for most of the infections found in South Africa's most populated province, Gauteng, over the last two weeks.
The number of cases of "appears to be increasing in almost all provinces" in the country, according to the WHO.
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South Africa reported 2,800 new infections on Sunday, a rise from the daily average of 500 in the previous week.
Government adviser and epidemiologist Salim Abdool Karim said he expected the number of cases to reach more than 10,000 a day by the end of the week, and for hospitals to come under pressure in the next two to three weeks.
Dr Phaahla said he wanted to "reiterate that there is absolutely no need to panic" because this "is no new territory for us".
"We are now more than 20 months' experienced in terms of Covid-19, various variants and waves," he added at a media briefing.
On Monday, Japan became the latest country to reinstate tough border restrictions, banning all foreigners from entering from 30 November.
The UK, EU and US are among those who earlier imposed travel bans on South Africa and other regional states.
The WHO has warned against countries hastily imposing travel curbs, saying they should look to a "risk-based and scientific approach".
The world body's Africa director Matshidiso Moeti said on Sunday: "With the Omicron variant now detected in several regions of the world, putting in place travel bans that target Africa attacks global solidarity."
However, Rwanda and Angola are among African states that have announced a restriction on flights to and from South Africa.
South Africa's foreign ministry spokesman Clayson Monyela described their decision as "quite regrettable, very unfortunate, and I will even say sad".
In a speech on Sunday, South Africa's President Cyril Ramaphosa said the bans would not be effective in preventing the spread of the variant.
"The only thing the prohibition on travel will do is to further damage the economies of the affected countries and undermine their ability to respond to, and recover from, the pandemic," he said.
Current regulations in South Africa make it mandatory to wear face coverings in public, and restrict indoor gatherings to 750 people and outdoor gatherings to 2,000.
Mr Ramaphosa said South Africa would not impose new restrictions, but would "undertake broad consultations on making vaccination mandatory for specific activities and locations".
There are no vaccine shortages in South Africa itself, and Mr Ramaphosa urged more people to get jabbed, saying that remained the best way to fight the virus.
Health experts said that Gauteng, which includes Johannesburg, had entered a fourth wave, and most hospital admissions were of unvaccinated people.
Omicron has now been detected in a number of countries around the world, including the UK, Germany, Australia and Israel.
In other developments:
China said it would offer 1bn doses of vaccines to African countries on top of the 200m it had already supplied
Separately, Dutch police said they detained a couple who had escaped from a quarantine hotel. According to the Dutch newspaper Het Parool, the Spanish man and Portuguese woman were arrested on a plane that was about to depart to Spain
Israel banned all foreigners from entering the country for 14 days from midnight on Sunday
The UK called for an emergency meeting of the G7 group of nations on Monday to discuss the new variant
Voters in Switzerland backed the government's measures to tackle Covid, according to preliminary results.
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