Citing an Allied security official from the scene at Kabul airport, the Reuters news agency reported that the evacuation of civilians was accelerated after the bombings in front of the airport and that the planes took off regularly.
The United States and its allies carried out one of the largest air evacuations in history. More than 100,000 people have been evacuated from Afghanistan since August 15, the White House said.
In his speech Thursday night, US President Joe Biden said more than 7,000 people had been evacuated in the last 12 hours, although it was not clear what had happened before the explosions that hit Kabul airport.
Washington is in a race against time to complete the evacuation before the August 31 deadline.
The United Kingdom said on Thursday it had evacuated more than 13,000 people from Afghanistan since the mission began.
More than 100 countries around the world have participated in these efforts. About 5,200 troops continue to secure Kabul airport.