The move is to allow for the evacuation of civilians trapped in the battle zone. Mr Lavrov said some 8,000 people would be taken out.
Government forces have retaken 75% of east Aleppo in recent weeks – areas rebels had controlled for four years.
A BBC reporter in Aleppo says while fighting appears to have eased, there is no sign it has completely stopped.
The US welcomed the “indication that something positive could happen but we’re going to have to wait and see whether those statements are reflected on the ground.
“Our approach to the situation has been to listen carefully to what the Russians say, but scrutinise their actions,” said White House spokesman Josh Earnest.
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Mr Lavrov said on the sidelines of a European foreign ministers meeting in Germany: “I can tell you that today, combat operations by the Syrian army have been halted in eastern Aleppo because there is a large operation under way to evacuate civilians.”
He also said Russian and US military experts would meet in Geneva on Saturday to discuss ways of bringing an end to the violence in Aleppo.
A US state department spokeswoman confirmed Mr Lavrov had spoken to John Kerry and both had agreed to discuss a ceasefire that allows for the delivery of aid and the departure of civilians, but the “specific nature” of Saturday’s technical talks “are still to be worked out”.
No sign fighting has stopped: BBC’s Lyse Doucet in Aleppo
Russia’s announcement comes at a time when tens of thousands of civilians have already been fleeing the fighting on their own, using whatever route they can. We saw a tide of people scrambling through a hole smashed through a wall.
News that the Syrian military has suspended operations to allow for a more orderly evacuation would be good news for tens of thousands of people still trapped inside rebel-held districts.
But while fighting appears to have eased, there’s no sign on the ground that it’s completely stopped. And pauses only succeed if they’re agreed by all sides and there’s no sign of that yet.
This week rebel fighters also called for a truce to allow civilians to leave the battlefield. But both sides suspect the other will use any pause to regroup for another round of fighting.
Earlier, a local council leader in Aleppo warned that “150,000 people are condemned to death” in the city.
Brita Haji Hassan, during a visit to UN officials in Geneva, said 800 people had been killed and up to 3,500 injured in the city in the past four weeks.
“We demand a safe passage for civilians to leave and an end to the killing, bombing and bloodbath,” he said.
Late on Wednesday, 148 mostly disabled and elderly civilians were evacuated from a former old people’s home in the Old City, hours after the area fell to government forces.
They were rescued in a joint operation by the Syrian Arab Red Crescent (SARC) and the International Committee of the Red Cross (ICRC).
Many had injuries or conditions which left them unable to move, and had been trapped in the home for days.
Eleven others had died before they could be reached, either caught in the crossfire or because of a shortage of medicine, officials said.
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The chairman of the UN’s humanitarian taskforce for Syria, Jan Egeland, praised the Red Cross operation as “heroic” but said evacuations should not “happen like that”. He instead called for the establishment of humanitarian corridors.
He told reporters in Geneva that he believed Russia and the US – which back opposing sides in the civil war – were still “poles apart” on agreeing terms.
The UN’s envoy for Syria, Staffan de Mistura, told reporters in New York on Thursday that he was planning to meet members of US President-elect Donald Trump’s team, though he did not say when.
Aleppo was once Syria’s largest city and its commercial and industrial hub before the uprising against President Bashar al-Assad began in 2011.
It has been divided in roughly two since mid-2012. But in the past year, Syrian troops have broken the deadlock with the help of Iranian-backed militias and Russian air strikes, reinstating a siege in early September.