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.
Taliban fighters seized Kabul on the weekend after a lightning offensive across the country as US-led Western forces have been withdrawing under a deal that included a Taliban promise not to attack them as they leave.
US forces running the airport had to stop flights on Monday after thousands of frightened Afghans swamped the facility looking for a flight out.
The situation was under control on Tuesday and flights resumed.