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The "overwhelming majority" of eligible people have now been evacuated from Afghanistan by the UK, the prime minister has said.
Boris Johnson said about 15,000 people had been flown out of the capital, Kabul, but that the time remaining for evacuation efforts was "quite short".
It comes amid a race to evacuate thousands before foreign troops depart.
Speaking during a visit to the British military's Permanent Joint Headquarters in north London, where he met troops involved in evacuation efforts, Mr Johnson said the UK's airlift would "keep going for as long we can".
He added: "In the time we have left, which may be - as I'm sure everybody can appreciate - quite short, we'll do everything we can to get everybody else."
The US has set a deadline of 31 August for the withdrawal of its troops, with President Joe Biden rejecting calls from Prime Minister Boris Johnson and other allies for an extension.
Kabul airport is currently being defended and run by the US, which has 5,800 troops on the ground - with the help of more than 1,000 UK troops.
Earlier, Armed Forces minister James Heappey declined to give a date for the last UK evacuation flights, but said it was likely that UK and other foreign troops would have to leave before the last American airlifts.
However, Mr Johnson insisted the US deadline would not mark the end of the UK's efforts to help people wishing to flee the Taliban-controlled country, adding that the current airlifts were just the "first phase".
"Even beyond the US deadline of 31 of this month, we hope to be able to continue to say to people, well you can come out."