Taliban Fateh fighters, a "special forces" unit, patrol along a street in Kabul on Sunday. AFP

The Taliban, Afghanistan's new rulers, and the departing US forces are aiming for a swift handover of Kabul airport as US forces are in the final phase of leaving Kabul, ending two decades of involvement in Afghanistan.

A Western security official said on Sunday that just over 1,000 civilians at the airport remain to be flown out before troops withdraw.

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Spokesman Zabihullah Mujahid said on Saturday the Taliban would take over the airport "very soon" after US forces withdraw and announce a full cabinet in the coming days.

Mujahid told Reuters the group had appointed governors and police chiefs in all but one of Afghanistan's 34 provinces and would act to solve the country's economic problems.

Taliban spokesperson Zabihullah Mujahid (right) listens to a question during a press conference in Kabul. AFP

The US-led invasion of Afghanistan in late 2001 overthrew the then-ruling Taliban as punishment for harbouring the al Qaeda militants behind the Sept. 11 attacks that year.

Meanwhile, Britain's last military flight left Kabul late on Saturday after evacuating more than 15,000 people in the two weeks since the Taliban took control of Afghanistan, ending nearly 20 years of British military presence in the country.

"The final flight carrying UK Armed Forces personnel has left Kabul," Britain's Ministry of Defence said.

A Taliban official told the media "We are waiting for the final nod from the Americans to secure full control over Kabul airport."

The official also said on condition of anonymity the militants, who seized control of the capital on Aug. 15 after a lightning advance against the Western-backed government, had a team of technical experts and highly qualified engineers ready to take over the airport.

UK military personnel onboard a A400M aircraft departing Kabul, Afghanistan, on Saturday. AP

President Joe Biden has said he will stick by his deadline to withdraw all US troops from Afghanistan by Tuesday.

"We want to ensure that every foreign civilian and those who are at risk are evacuated today. Forces will start flying out once this process is over," said the official, who is stationed at the airport.

A US official told the local media reporters that there were fewer than 4,000 troops left at the airport, down from 5,800 at the peak of the evacuation mission.

US President Joe Biden pauses as he speaks about the bombings at the Kabul airport in Washington. File/AP

Britain on Friday had said its evacuation mission would end within hours and that its military would be unable to fly out any Afghan citizens eligible for resettlement who had not already entered Kabul airport.

"We should be proud of our armed forces, welcoming to those coming for a better life and sad for those left behind," Defence Minister Ben Wallace said after the final British flight.