Afghans gather on a roadside near the military part of the airport in Kabul. AFP

At least seven civilians have been killed as tens of thousands of Afghans were racing on Sunday to flee their country. In the week since the Taliban took back power in Afghanistan, the Taliban have vowed a softer version of their brutal rule from 1996-2001, and taken steps towards forming a government.

The United States warned of security threats at Kabul's chaotic airport and the European Union said it was "impossible" to evacuate everyone at risk from the Taliban.

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On Saturday, the United States and Germany told their citizens in Afghanistan to avoid travelling to Kabul airport, citing security risks as thousands of desperate people gathered trying to flee.

The airport has been the focal point for thousands trying to flee the Taliban, who swept into Kabul a week ago after their lightning advance seized the country.

US soldiers stand guard behind barbed wire as Afghans sit on a roadside near the military airport in Kabul. AFP

Britain's Sky News on Saturday aired footage of at least three bodies covered in white tarpaulin outside the airport. It was not clear how they had died.

Sky reporter Stuart Ramsay, who was at the airport, called the deaths "inevitable" and said people were being "crushed", while others were "dehydrated and terrified".

The footage was the latest image of utter despair, after video of a baby being lifted over a wall at the airport and horror scenes of people hanging onto departing planes.

Families hoping for a miracle crowded between the barbed-wire that surrounds an unofficial no man's land separating the Taliban from US troops. Roads to the airport were choked with traffic.

President Joe Biden has described the situation as "one of the largest, most difficult airlifts in history".

Circumstances were further complicated on Saturday when the US government warned its citizens to stay away from the airport.

No specific reason was given, but a White House official later said Biden had been briefed on "counter terrorism" threats, including the Daesh group.