Secretary General Jens Stoltenberg, speaking after a video conference of NATO foreign ministers, also said some allies were pushing for more time to complete their evacuations.

The United States -- which has overall control of operations at the airport -- had previously set an August 31 deadline to pull its forces out of Afghanistan.

But several other NATO countries raised the possibility of that now being pushed back, given the evacuations.

Their citizens and vulnerable Afghans who worked for international missions are still trapped in the country, which has fallen to Taliban control.

NATO itself still has 500 civilian staff, including nearly 200 Afghans, working at the airport to keep it open while national military rescue operations continue.

"The big challenge is to get people on those planes," Stoltenberg told reporters, urging the Taliban not to prevent foreign and Afghan would-be evacuees from approaching the airport.

"We have more planes than we have people or passengers because the process of getting people -- especially Afghans -- into the airport and processed is now the big, big challenge," he said.

Many allies, he said, had stressed the "need to work harder on how can we get more people who are now outside the airport".

After the videolink meeting, NATO's 30 members issued a statement calling on "those in positions of authority in Afghanistan to respect and facilitate their safe and orderly departure.

"As long as evacuation operations continue, we will maintain our close operational coordination through allied military means at the airport," they said.

But how long that allied military deployment remains at the airport is open to question.

The United States provides the bulk of the forces defending the perimeter of what has become Afghanistan's last link to the outside world, and last hope for refugees.

- Extending deadline -

Britain and Turkey also have military contingents at the airport -- and Germany, France and other allies have been relying on the facility as they run missions to secure evacuees.

"That was an issue that was discussed during the meeting today, and several allies raised the issue of potentially extending the timeline to get more people out," Stoltenberg said.

"The US has stated that the timeline ends on August 31, but several of our allies raised during the discussion today the need to potentially extend that to be able to get more people out."

Taliban fighters control all access roads and a UN report suggests that the group is going door-to-door in Kabul hunting for those who worked with NATO diplomats and militaries.

Most capitals have not formally recognised the Taliban as Afghanistan's new government, but Stoltenberg said some NATO allies have established "operational tactical contact" with the group.

"That is to ensure safe passage to manage the situation outside the airport and so on," he said.

He added: "We have to distinguish these kinds of tactical operational contacts with the Taliban... and diplomatic recognition. That's two different things."