Boris Johnson has said his immediate priority is to get UK nationals and those who helped the nation out of Afghanistan "as fast as we can".
Almost 2000 Afghans, including translators who supported the military, have already been resettled in the UK, but many more have been left behind or faced with leaving their families.
In a television clip following an emergency Cobra meeting, the PM said: "We're going to get as many as we can out in the next few days".
"Our priority is to make sure that we deliver on our obligations to British nationals in Afghanistan, all those who helped the British effort in Afghanistan over 20 years," he said
"The ambassador has been there at the airport to process the applications".
Mr Johnson said it was "clear that very shortly" there would be new government in Kabul and the West must "collectively" make clear that it must not allow terrorism to breed there.
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"Nobody wants Afghanistan to once again be a breeding ground for terror. We don't think that's in the interests of the Afghan people that it should lapse back into that pre-2001 state".
He denied that the speed of the Taliban incursion had caught the Government by surprise, after he told MPs last month there was "no military path to victory" for the group.
"It's very clear from what I said the situation in Afghanistan was going to change," he said.
"It's fair to say the US decision to pull out has accelerated things. But we've known for a long time that this was the way things were going".
Mr Johnson denied throwing human rights out of the window after the Taliban confirmed it would bring back Sharia law.
"We continue to attach huge importance to human rights and equalities," he said.
"A lot of women and girls were educated thanks to the UK... a lot of rights were promoted in a way that Afghanistan hadn't seen before. We don't want that thrown away."
But Labour former defence secretary George Robertson, who was Nato secretary general during the September 11 attacks, said: "I am sickened by the prospect of the 20th anniversary being marked by the Taliban back in control of Afghanistan.”
Lord Roberts added: “It is stunning that the Foreign Secretary would stay on holiday as our mission in Afghanistan disintegrated.
"The horrors unfolding with every minute demand focused attention from the top.
"The urgency involves both the evacuation of British citizens but also what is now to happen to the people of Afghanistan.
"The fact that the Foreign Secretary is missing in action shows graphically the lack of purpose in our government’s attitude to what we set out to do twenty years ago."
Speaker of the House, Sir Lindsay Hoyle, has already granted a request by Government to recall MPs, the Commons authorities have said on Sunday.
The parliamentary authorities said: "The Speaker of the House of Commons has granted a request from the Government to recall the House at 9.30am - 2.30pm on Wednesday August 18 in relation to the situation in Afghanistan."
Mr Johnson is facing calls to stage a last-ditch intervention as the Taliban sweeps across the Middle Eastern country.
The hardline group already controls large swathes on Afghanistan and entered its capital, Kabul, on Sunday.
The country's president Ashraf Ghani has already left the city for Tajikistan, a senior Afghan Interior Ministry official confirmed.
And other nations are scrambling to remove their embassy staff as the Taliban - which follows an austere version of Islam - takes charge.
The chaos comes after US President Joe Biden announced in April that the remaining 2,500 US troops would leave Afghanistan by September 11 - the 20th anniversary of the 9/11 attacks.
Other Nato allies then confirmed they would follow suit, including Britain - which in May began withdrawing its remaining 750 military trainers.
But there is deep anger among many MPs at the way Afghanistan is being abandoned to its fate.
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The chairman of the Commons Foreign Affairs Committee Tom Tugendhat said it was "the biggest single foreign policy disaster" since Suez, while Defence Committee chairman Tobias Ellwood said it was a humiliation for the West.
Labour leader Sir Keir Starmer said ministers needed to explain what they intended to do to avert a looming humanitarian crisis and prevent Afghanistan again becoming a base for international terrorism.
Mr Ellwood said it was still not too late to turn the situation around, and called for the despatch of the Royal Navy carrier strike group to the region, urging the Prime Minister to convene an emergency conference of "like-minded nations" to see what could be done.
Mr Tugendhat, who served as an Army officer in Afghanistan, said the priority had to be to get as many people out as possible before Kabul collapsed.
