Seven people died during the chaos at the Kabul airport, some of which were seen on a video shared on social media showing people falling from a departing U.S. Air Force C-17 transport plane.
Another video shows civilians hanging on to the undercarriage as the plane takes off.
Many of them fear chaos and the return of the brutal rule the Taliban imposed when it was last in power, especially after the Taliban freed thousands of prisoners and the police simply melted away.
At least five people were killed at the airport earlier Monday, as hundreds of people tried to forcibly enter planes.
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.
Massouma Tajik, a 22-year-old data analyst, told AP that U.S. troops also sprayed gas to disperse the crowds after people swarmed onto the tarmac.
U.S. Deputy National Security Adviser said more forces are will be sent into Kabul Airport today and tomorrow.
The chaotic scenes come as the Taliban declared the war in Afghanistan was over, taking control of the presidential palace in Kabul.
President Ashraf Ghani fled the country on Sunday as the Islamist militants entered the capital virtually unopposed, saying he wanted to avoid bloodshed, while hundreds of Afghans desperate to leave flooded Kabul airport.