"Turkish-Russian-Iranian cooperation ensures the evacuation of civilians and armed groups from eastern Aleppo," said Lavrov.
He added that he hoped the evacuation process would "end" in a day or two.
|Analysis: After the assassination - what next for Russia and Turkey?|
According to Turkish Foreign Minister Mevlut Cavusoglu, a total of 37,500 have already been evacuated from Aleppo. An estimate from the International Committee of the Red Cross earlier on Tuesday put the figure at 25,000.
Cavesoglu also emphasised Turkey's support for the Russia-Turkey-Iran format for resolving Syria's crisis, adding that Ankara would continue its efforts in the war-torn country.
"The best solution is political solution. We believe in this. We have to focus on this," he said.
Tuesday's joint declaration marked a positive step for cooperation between Ankara and Moscow, following the assassination of Russian envoy Andrei Karlov in the Turkish capital on Monday. The killing comes months after Russia and Turkey began strengthening ties that had seized up over the downing of a Russian jet in Syria.
"We know that this is a provocation aimed at destroying the process of normalisation in relations between Turkey and Russia," Russian President Recep Tayyip Erdogan said in televised comments on Monday.
Russia and Iran sit on the opposite side of the Syrian conflict from Turkey, with Moscow and Tehran backing Syrian President Bashar al-Assad and Ankara supporting those seeking to topple him.
Despite this, cooperation between Moscow and Ankara has increased in recent months, with Turkey having recently denied that it forged a secret "bargain" with Russia over the future of Syria.
This followed improved cooperation that led to a deal for evacuations from war-wrecked Aleppo.