Afghan refugees arrive at Dulles International Airport in Dulles, Virginia, US, on Tuesday. Reuters

Britain has opened talks with the Taliban over the "safe passage" of its remaining nationals and allies out of Afghanistan as US Secretary of State Antony Blinken was leading continued diplomatic efforts to ensure safe passage for any American, Afghan partner or foreign national who wanted to leave Afghanistan after the Aug. 15 takeover by the Taliban.

The White House on Tuesday said 98 per cent of Americans who wanted to leave Afghanistan were able to do so, and President Joe Biden affirmed that the United States remained committed to helping the remaining 100 to 200 US citizens who had some intention to leave.

The British government confirmed to the media that it has dispatched senior civil servant Simon Gass to meet with Taliban representatives in Doha.

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Much of the group's senior leadership lived in exile in the Qatari capital until the overthrow of Afghanistan's Western-backed government after 20 years of war.

Prime Minister Boris Johnson has come under fire after many Afghans who helped NATO — and are eligible to move to Britain — were believed to have been left stranded in Afghanistan, where they are at the mercy of the Taliban.

Evacuees wait to board during an evacuation at Hamid Karzai International Airport in Kabul. File/Reuters

Meanwhile, speaking at the White House, Biden told reporters the international community would hold Taliban leaders accountable for their promise to permit freedom of travel.

"The Taliban has made public commitments, broadcast on television and radio across Afghanistan, on safe passage for anyone wanting to leave, including those who worked alongside Americans," he said. "We don't take them by their word alone, but by their actions, and we have leverage to make sure those commitments are met."

In the end, the president said, more than 5,500 Americans were evacuated, along with thousands of citizens and diplomats from allied countries, as well as 2,500 locally employed staff at the US embassy and their families, and thousands of Afghan translators and interpreters and others who supported the United States.

The Taliban has pledged to allow Afghans to come and go in the face of calls from the international community to honour that commitment in the days after the US withdrawal on Tuesday.

Prime Minister Boris Johnson speaks during a meeting in London. File photo

More than 8,000 Afghans who helped NATO forces made it out of Afghanistan and the British government said they would be given indefinite leave to remain.

But criticism was levelled at the government for not evacuating hundreds more stuck in the war-torn country as the Taliban took control.

British Foreign Minister Dominic Raab was also condemned by the opposition Labour party for not immediately leaving a beach holiday when the Taliban took control.

An unnamed British minister told the Sunday Times that he believed the UK could have evacuated "800-1,000 more people" in the chaotic airlift.

Johnson's government sought to extend the US withdrawal deadline of August 31 but ultimately failed to persuade President Joe Biden.

After the Taliban swept into Kabul in mid-August, the British premier said the Taliban must be judged on its "actions rather than by its words" and insisted Britain could not have remained in Afghanistan without American support.