At least 12 people have been killed in and around the airport in Kabul, Taliban and Nato officials said, since the Taliban seized the city on Sunday, triggering a rush of fearful people trying to leave.
The deaths were caused either by gunshots or in stampedes, the Taliban official said on Thursday, and he urged people still crowded at the gates of the facility to go home if they did not have the legal right to travel.
"We don't want to hurt anyone at the airport," said the Taliban official, who declined to be identified.
The previous day, seventeen people were injured in a stampede at a gate to the airport, said a Nato security official working at the airport. He added that Afghan civilians had been told not to gather around the airport unless they had a passport and visa to travel.
Witnesses said Taliban members had prevented people from getting into the airport compound, including those with the necessary documents to travel.
"It's a complete disaster. The Taliban were firing into the air, pushing people, beating them with AK47s," said one person who was trying to get through.
A Taliban official said commanders and soldiers had fired into the air to disperse crowds outside Kabul airport, but told Reuters: "We have no intention to injure anyone."
According to witnesses, the situation was calmer on Thursday.
The United States and other Western powers pressed on with the evacuation of their nationals and some of their Afghan staff from the capital's airport, from where about 8,000 people have been flown out since Sunday, a Western security official said.
US forces running the airport had to stop flights on Monday after thousands of frightened Afghans swamped the facility looking for a flight out. Senior US military officials said the chaos had left seven people dead, including some who fell from a departing American military transport jet.
Flights resumed on Tuesday as the situation came under control.
Under a pact negotiated last year by former President Donald Trump's administration, the United States agreed to withdraw its forces in exchange for a Taliban guarantee they would not let Afghanistan be used to launch terrorist attacks.
The Taliban also agreed not to attack foreign forces as they left.
US President Joe Biden said US forces would remain until the evacuation of Americans was finished, even if that meant staying past an August 31 US deadline for withdrawal.