The United States and more than 90 countries and organizations say they have received assurances from the Taliban on the safe departure of those who want to leave Afghanistan.
The White House released a joint international statement on Sunday with Japan, Britain, the European Union and many other countries and organizations.
The statement says, "We have received assurances from the Taliban that all foreign nationals and any Afghan citizen with travel authorization from our countries will be allowed to proceed in a safe and orderly manner to points of departure and travel outside the country."
It also says those countries will continue issuing travel documentation to designated Afghans.
But some experts say it is unclear whether visas can be issued to applicants as many foreign embassies in Afghanistan have shut down.
Tensions remain high in Kabul after more than 100 people were killed in a suicide bomb attack near the airport in the capital on Thursday.
The US military carried out a drone airstrike on Sunday on an explosive-laden vehicle. It said the action was aimed at eliminating terror threat to the airport.
The US has set a deadline of August 31 for its withdrawal from Afghanistan.