Turkish President Recep Tayyip Erdogan urged Russian counterpart Vladimir Putin on Saturday to maintain dialogue with the Taliban and to take a "gradual" approach to relations with Afghanistan's new rulers.

"We must keep the channels of open dialogue with the Taliban and pursue a gradual engagement instead of an approach based on hard conditions," Erdogan said in a phone call with Putin, according to a statement from his office. 

The Turkish leader also welcomed talks between the Taliban and former senior Afghan officials as "promising". 

"We welcome the Taliban's moderate messages as positive for the moment, but the process ahead will be shaped not by their words but by their deeds," Erdogan said. 

"The presidents agreed to strengthen bilateral cooperation on Afghanistan," the Kremlin said in a statement. 

According to Moscow, the two leaders affirmed the need to ensure "stability and a peaceful society in the country" with an emphasis on "the fight against terrorism and drug trafficking".

Turkey, which has several hundred troops in Afghanistan, is involved in securing Kabul airport with the United States. 

In July, Ankara offered Washington to take over the airport after the withdrawal of US troops.

That plan appeared to be in jeopardy with the return of the Taliban, who have publicly warned Turkey against keeping its troops there. 

"We can continue to secure and manage Kabul airport if the right conditions emerge," the Turkish leader said on Saturday.