Both the leaders have emphasised the need to prevent any violations of ceasefire deal.
Turkish President Tayyip Erdogan and Russian counterpart Vladimir Putin agreed in a telephone call on Wednesday to make a joint effort to start the evacuation of civilians and opposition forces from eastern Aleppo as soon as possible.
Anadolu Agency reported quoting presidential sources that both the leaders emphasised the need to prevent the violations of a ceasefire deal.
A truce deal was reached between Ankara and Moscow on Tuesday night to allow civilians trapped in eastern Aleppo to evacuate from the rebel-held districts on Wednesday morning. The evacuation did not begin and renewed fighting risks collapse of the ceasefire.
Erdogan told Putin that Turkey was ready to take all possible measures to provide temporary shelter and humanitarian aid following the opening of safe corridors.
Earlier on Wednesday, Erdogan accused Syrian regime forces of breaking the ceasefire, but said Turkey is still making efforts to create a corridor to evacuate people from the Syrian city.
He accused the Assad regime of committing war crimes in Aleppo and called on the international community to support the ceasefire.
"The realisation of the ceasefire brokered by Turkey is perhaps the last hope for the innocent people in Aleppo," he said, in a televised speech in Ankara.
"This humanitarian corridor must be opened immediately, and the evacuation of civilians from eastern Aleppo must be allowed at once. Assad regime is committing war crimes in eastern Aleppo, and everybody including those who support him has to see this."
The planned evacuation was stalled after the fighting on Wednesday in eastern Aleppo and Iran put new conditions on the ceasefire deal.
Iran, a key backer of the Syrian regime, wants a simultaneous evacuation of wounded from the villages of Foua and Kefraya that are besieged by rebels, according to opposition and UN sources.