The footage posted by Afghanistan's largest private broadcaster, Tolo news, highlighted the chaos at Hamid Karzai International Airport after Taliban fighters entered Kabul following the withdrawal of foreign forces.
Reuters was not immediately able to verify the footage or reports that some people were killed falling from aircraft.
At least five people died as the chaos mounted at the airport, according to witnesses, though one person waiting for a flight told Reuters it was unclear whether those killed had been shot or trampled in a stampede.
US troops fired warning shots to stop people getting on flights taking out diplomats and embassy employees, and two gunmen were also shot at the airport, US officials told Reuters.
The flights were later halted because of the chaos, with Germany saying it had to divert its first of three planned evacuation flights to the Uzbek capital Tashkent because it could not land due to the throngs of people on the tarmac.
Pentagon spokesperson John Kirby said US forces were working with Turkish and other international troops to clear Kabul airport to allow evacuation flights to resume. He said several hundred people had been flown out so far.
Videos and photos posted on social media showed hundreds of civilians invading the airport's single runway, jostling to climb stairs onto overhead gangways and sitting on the top of passenger jets in the hope of getting a flight out.
"This is our airport but we are seeing diplomats being evacuated while we wait in complete uncertainty," Rakhshanda Jilali, an Afghan human rights activist who was trying to get to Pakistan, told Reuters in a message from the airport.
A US State Department spokesperson said all embassy personnel, including Ambassador Ross Wilson, had been transferred to the airport to await evacuation.
One video showed a military helicopter flying low to pave a path for a plane trying to take off through crowds of people.
Local news agency Asvaka reported that some people who had clung to the outside of a plane plunged to their deaths after it took off. Reuters could not verify the report or footage shared by the agency.
One witness said he had seen five bodies piled up in a vehicle. A video posted on social media showed three bodies on the ground near what appeared to be an airport side entrance. Tolo news reported at least 10 people had died at the airport.
Reuters could not verify the footage or the report.
