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.
The US welcomed the “indication that something positive could happen but we’re going to have to wait and see”.
“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.
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.
‘Bombing and bloodbath’
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 died before they could be reached, either caught in the crossfire or because of a shortage of medicine, officials said.
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.
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.
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