Lavrov's remarks came following a trilateral meeting on Syria with his Iranian and Turkish counterparts, Javad Zarif and Mevlut Cavusoglu in Moscow.
He said a joint declaration was agreed on to find a solution in Syria.
"Turkish-Russian-Iranian cooperation ensures the evacuation of civilians and armed groups from eastern Aleppo," said Lavrov.
He said he hoped evacuations would end in one or two days.
Lavrov said the trilateral format was effective.
"The most efficient and effective format for solving the Syrian crisis is our current trilateral format," he added.
Turkey’s Mevlut Cavusoglu said a total of 37,500 people have been evacuated from Aleppo so far.
"The best solution is a political solution. We believe in this. We have to focus on this," said Cavusoglu.
Cavusoglu said the countries will continue their efforts for Syria.
"We will continue together to pursue our efforts to stop bloodshed in Syria, spread a permanent cease-fire throughout the country, and unhindered humanitarian aid," he added.
He said they discussed expanding the cease-fire to the entire country.
"We can reach a solution in Syria if we sincerely implement the decisions taken," said Cavusoglu.
He reiterated that Turkey supports the national unity and territorial integrity of all of its neighbors.
Iran’s Zarif said the international community should cooperate on counter-terrorism and that violence in Syria needs to be prevented.
"The evacuation of civilians and armed groups from some regions has succeeded thanks to the collaboration between Russia, Iran, and Turkey," he added.
Zarif said he hoped a political solution could be reached in Syria. "We will strive to ensure territorial integrity and sovereignty," he said.
In recent weeks, numerous reports have emerged of violence being perpetrated against civilians in Aleppo, once considered an opposition stronghold.
The evacuation process was temporarily suspended on Friday after pro-regime foreign terrorist groups attacked a civilian convoy leaving the city, resulting in a number of evacuees getting killed.
It resumed Monday under an earlier deal brokered by Turkey and Russia according to which some 20,000 civilians and fighters are to be evacuated from eastern Aleppo on Monday and Tuesday.