The evacuations were the first made public by Russia, which has taken a cautiously optimistic outlook of the new Taliban leadership in Kabul.

Moscow said it sent four military transport planes to fly out more than 500 citizens of Russia, Belarus, Kyrgyzstan, Tajikistan, Uzbekistan and Ukraine.

The evacuations were being organised at the behest of President Vladimir Putin and Defence Minister Sergei Shoigu, Russia's military said in a statement.

Each plane had drinking water, individual rations and blankets for the evacuees, the statement added.

While Belarus, Kyrgyzstan, Tajikistan and Uzbekistan are members of a Moscow-led security bloc, Ukraine and Russia have had strained ties since Moscow in 2014 annexed Crimea and pro-Russia separatists broke away in the east.

Unlike Western countries, Russia has not evacuated its embassy in Kabul, having secured guarantees of the mission's protection from the militants.

Last week Russia's ambassador to Afghanistan Dmitry Zhirnov said the Taliban were "engaged in restoring order" in Kabul and were behaving in a "responsible, civilised manner".

But on Tuesday the Kremlin suggested that some of the embassy staff's families -- women and children -- may have been taken out of Afghanistan.

Russia in recent years has reached out to the Taliban and is seeking contact with the group to stop the instability from spilling over into Central Asia where Moscow maintains military bases.

While some countries have welcomed Afghan refugees fleeing the Taliban, Putin has warned against an influx into Russia, saying militants could enter the country under the guise of seeking asylum.