Over 2,200 diplomats and other civilians have so far been evacuated on military flights out of Kabul, a Western security official in the Afghan capital told Reuters on Wednesday.
There was no clarity yet on when civilian flights will resume from Kabul, the official said.
In addition, Britain has managed to remove around 1,000 people a day from Afghanistan after the Taliban seized control of the country, interior minister Priti Patel said on Wednesday.
"We have been getting out approximately 1,000 people, so far, a day," she told BBC TV.
"We're still bringing out British nationals... and those Afghan nationals who are part of our locally employed scheme."
Poland has evacuated around 50 people from Afghanistan, a deputy foreign minister said on Wednesday, part of an international effort to get diplomats and other civilians out of the country after Taliban insurgents seized the capital.
Poland said on Tuesday it had around 100 people on an evacuation list. It has pledged offer places on its planes to other people trying to leave Afghanistan from Kabul airport, where chaotic scenes have caused problems for some evacuation efforts.
"About 50 people were evacuated from Afghanistan, they are now safe in the care of the Polish consulate in Uzbekistan," Marcin Przydacz told reporters. "A civilian plane is waiting for them that will soon transport them to Poland."
Przydacz said that one Polish citizen was among those evacuated, while the others were people who had worked with the Polish military and diplomatic missions.
Also, 25 French nationals and 184 Afghans were evacuated from Afghanistan overnight and have just landed in Abu Dhabi, French Foreign Affairs Minister Jean-Yves Le Drian said on Wednesday.
Hungary said on Wednesday it had organized the evacuation of a group of 26 Hungarian nationals working as contractors from Afghanistan, and they would return to Hungary shortly on a flight organized by another country.
In addition, the country is sending its own evacuation mission to Afghanistan to help other Hungarians still in Kabul, deputy foreign minister Levente Magyar told a news conference.
Other Afghans who arrived in Germany on Wednesday described chaotic and terrifying scenes at Kabul airport before they were evacuated to safety, and said they feared for the lives of loved ones they left behind.
Speaking shortly after landing in Frankfurt on a flight from Tashkent, men, women and children said they were part of a lucky few evacuated by NATO armies after the country fell to the Taliban with astonishing speed.
"We had to force our way through and my little son fell over, and we were scared, but we made it," said a woman, speaking in German.