The US says it will keep evacuating Afghans from Kabul airport until "the last moment", despite continuing concerns about attacks from the Islamic State (IS) group.
Reports from Kabul now suggest as many as 170 people died in Thursday's attack on crowds at a gate to the airport.
The Pentagon says there are still credible threats against the airport.
The US is still processing Afghans desperate to leave. Most Nato countries have now ended their emergency flights.
France ended its evacuation effort on Friday, blaming deteriorating security at the airport. It said it had flown nearly 3,000 people out of the country.
The deadline set by the US for its forces to leave Afghanistan expires on 31 August.
BBC's chief international correspondent Lyse Doucet, who is in Kabul, has been told by sources that the US and British troops are "wrapping up" at the airport, and that the Taliban will take over in "a matter of hours".
A spokesman for the Taliban said on Friday night they had now taken control of parts of the airport. However, the Pentagon disputed this.
According to the Pentagon, more than 5,000 people remain inside the airport, waiting to be flown out. Officials also said measures had been implemented, in conjunction with the Taliban, to improve safety.
The White House says more than 111,000 people have been evacuated since the airlift began nearly two weeks ago.
The mission, a White House official said, would prioritise the remaining American citizens who wanted to leave, with US forces "engaged in a variety of means to get them to the airport safely".
Meanwhile, the US Embassy in Kabul advises American citizens to avoid travelling to the airport and avoid the airport's gates because of security threats.
The attack on Kabul airport was carried out by a suicide bomber who walked into the crowd of families waiting outside one of the gates, according to UK Defence Secretary Ben Wallace.
There was no second blast near an airport hotel, as originally thought, US officials said on Friday.
Dozens of Afghans were killed - a final number has yet to be established. In addition, 13 US personnel, two British nationals and the child of a British national were among the dead.
Some victims were blown into a sewage canal where Afghans were waiting to be processed, while dozens were rushed to hospital.
Hospitals in Kabul, already struggling with fewer staff since the Taliban took power nearly two weeks ago, have been overwhelmed with patients.
Wounded US personnel were flown to an American airbase in Germany.
Meanwhile, US President Joe Biden has been warned that another terror attack in Kabul is likely in the coming days.
The next few days would be "the most dangerous period to date", a White House official said, adding that US forces were looking at possible IS targets.
IS-K, or Islamic State Khorasan Province, is the group that claimed to be behind Thursday's deadly airport attack.
It is the most extreme and violent of all the jihadist militant groups in Afghanistan. Pentagon spokesman John Kirby said the US took the group "very seriously".
"Obviously they are a serious terror threat," he said, adding: "I think the threat is real and nobody wants to see that threat grow.
"We're not going to allow attacks on the homeland to emanate from Afghanistan again like they did 20 years ago."
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