Taliban militants controlling access to the airport have fired shots into the air to disperse approaching crowds.
Some 5,000 people have been evacuated in the last 24 hours, through the airport which is being run by US troops deployed to organise the evacuation.
It comes three days after the Taliban takeover of Afghanistan.
"It's absolutely hectic and chaos out there," one Western official told the Reuters news agency, as thousands of people remain desperate to leave, including Afghans who helped the US-led mission in the country over the past 20 years.
