US and allied forces have mounted a massive two-week effort to ferry foreign nationals and tens of thousands of vulnerable Afghans out of the country.
The airlift - one of the biggest such evacuation operations ever - marked the end of a 20-year Western mission in Afghanistan that began when US-led forces ousted a Taliban government that had provided safe haven for the perpetrators of the Sep 11, 2001, attacks on the United States.
The final chapter came quickly after the US and the Taliban made a deal to end the foreign involvement.
The Western-backed government and Afghan army melted away as Taliban fighters swept across the country and took control of Kabul on Aug 15.
The United States and allies have taken about 113,500 people out of Afghanistan in the past two weeks, but tens of thousands who want to go will be left behind.
"We tried every option because our lives are in danger. (The Americans or foreigners) must show us a way to be saved. We should leave Afghanistan or they should provide a safe place for us," said one woman outside the airport.
A Taliban official told Reuters that the Islamist group had engineers and technicians ready to take charge of the airport.
"We are waiting for the final nod from the Americans to secure full control over Kabul airport as both sides aim for a swift handover," said the official, speaking on condition of anonymity.
Britain's last military flight left Kabul on Saturday night after a chaotic two weeks at the airport that was plunged into a bloodbath on Thursday when an Islamic State suicide bomb attack outside the airport gates killed at least 90 Afghans and 13 American troops.
British Prime Minister Boris Johnson defended the evacuation operation, but he faced accusations that his government had been "asleep on watch".
FINANCIAL AND HUMANITARIAN CRISIS
The collapse of the government leaves an administrative vacuum that has led to fears of an economic crisis and widespread hunger.
Prices for commodities like flour, oil and rice are rapidly rising and the currency is plunging, with money changers across the border in Pakistan already refusing to accept the afghani.
On Saturday, officials ordered banks to reopen and imposed a limit on withdrawals of US$200 or 20,000 afghani. Long queues of people trying to withdraw money formed outside bank branches.
Taliban spokesman Zabihullah Mujahid has said that the difficulties will subside quickly once the new administration is up and running.
But with its economy shattered by 40 years of war, Afghanistan is now facing the end of billions of dollars in foreign aid poured in by Western donors.
Mujahid said that the Taliban would announce a full Cabinet in the coming days. It had appointed governors and police chiefs in all but one of Afghanistan's 34 provinces, he said.
It also appealed to the United States and other Western nations to maintain diplomatic relations after withdrawing. Britain said that should happen only if the Taliban allow safe passage for those who want to leave and respect human rights.
The Taliban's 1996 to 2001 rule was marked by a harsh version of sharia, Islamic law, with many political rights and basic freedoms curtailed and women severely oppressed.
Afghanistan was also a hub for anti-Western militants, and Washington, London and others fear it might become so again.
While Kabul's airport has been in chaos, the rest of the city has been generally calm. The Taliban have told residents to hand over government equipment including weapons and vehicles within a week.
The Western security official said that crowds at the airport gates had diminished after a specific warning from the US government of another attack by ISIS-K, the branch of Islamic State in Afghanistan that is an enemy of both the West and the Taliban.
The United States said on Saturday that it had killed two ISIS-K militants. Biden had vowed to hunt down the perpetrators of the explosion and said that the strike was not the last.
The Taliban condemned the US drone strike, which took place in Nangarhar province, an eastern area that borders Pakistan.
The airport attack added fuel to criticism Biden faced at home and abroad for the chaos. He has defended his decisions, saying that the United States had long ago achieved its rationale for invading in 2001.
Johnson said that Britain would not have wished to leave Afghanistan in such a manner. But Richard Dannatt, a former head of the British Army, said that the British government needed to investigate why it was so ill-prepared for the rapid fall of Afghanistan to the Taliban.
"It is unfathomable why it would appear that the government was asleep on watch," Dannat told Times Radio.