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.
One minister warned earlier that there could be a “highly lethal” terror attack at Kabul airport within hours.
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.”
Mr Johnson said of the rescue mission: “There’s been nothing quite like it in terms of speed and scale in our lifetimes, certainly in my memory.”
He said we “owe a debt” to those Afghans who had “helped for the 20 years of the UK’s engagement in Afghanistan” and that work was continuing to find them homes and ways to “integrate into our society”.
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.”
The prime minister admitted that although the “lion’s share” of eligible people had been airlifted from the country, he recognised “there will be people who still need help”.
Challenged on the suggestion that people who cannot enter the airport should travel to borders by road – which are reportedly being blocked by the Taliban – Mr Johnson said the G7 leaders were hoping the Taliban understands that “safe passage for those who want to come out is the key precondition” if they want to “engage with development aid” and have a relationship with the outside world.
His comments come after the UK Foreign Office issued new guidance that people should stay away from Kabul airport due to a “high threat of a terrorist attack”.
The FCDO urged anyone in the area to “move away to a safe location and await further advice”. Australia and the US also issued alerts, telling those outside the airport to leave immediately.
In the update issued on Wednesday evening, the FCDO also warned that travelling by road was “extremely dangerous” with people alleged to have been “mistreated” on their way to the airport.
Mr Heappey said earlier that there were “very credible” reports of a “severe” threat in the capital.
He told BBC Breakfast: “The credibility of the reporting has now reached the stage where we believe that there is a very imminent, highly lethal attack possible within Kabul.”
Asked by Sky News whether an attack could occur in the coming few hours, Mr Heappey replied: “Yes.”
He told the BBC the threat had created an “extraordinarily challenging situation, both on the ground and as a set of decisions to be taken in Whitehall”.
“People are desperate, people are fearing for their lives anyway, and so I think there’s an appetite among many in the queue to take their chances,” he said.