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.