One witness said he had seen the bodies of five people being taken to a vehicle. Another witness said it was not clear whether the victims were killed by gunshots or in a stampede.
U.S. troops, who are in charge of the airport, earlier fired in the air to scatter the crowd, a U.S. official said.
Officials were not immediately available to comment on the deaths.
As we reported earlier, Taliban fighters took control of the entire territory of Afghanistan on Sunday, August 15th.
President left, Kabul airport came under fire, Taliban took control of the presidential palace.
The United Nations Security Council scheduled an emergency meeting for Monday morning after the Taliban appeared to take control of Afghanistan. The decision was made at the request of Estonia and Norway.
Council diplomats said Sunday that UN Secretary-General Antonio Guterres will brief council members on the latest situation following the Taliban takeover of the capital, Kabul.