Syrian government forces and their allies drove rebels from a major eastern Aleppo neighborhood and several smaller areas Monday, state media reported.
Capturing rebel-held eastern Aleppo would be the biggest victory for President Bashar al-Assad since the start of the Syrian uprising in 2011.
Russia's Defense Ministry said the areas captured by Syrian government troops include 10 neighborhoods and more than 3,000 buildings.
The ministry said in a statement that more than 100 rebels had laid down their arms and exited the Syrian city's eastern suburbs.
Aleppo, Syria's largest city and former commercial center, has been contested since the summer of 2012 and a rebel defeat in the city would be a turning point in the five-year conflict.
If Syrian forces capture all of east Aleppo, Assad's government will be in control of the country's four largest cities as well as the coastal region.
The government's push, backed by thousands of Shiite militia fighters from Lebanon, Iraq, and Iran, and under the occasional cover of the Russian air force, has laid waste to Aleppo's eastern neighborhoods.
Syria's state news agency SANA said government forces captured the Sakhour neighborhood early Monday morning.
Speaking to Reuters, one rebel official denied the report that Sakhour had fallen, an advance that would cut the rebel-held eastern districts of Aleppo in two. Another told the news agency that the situation was not yet clear.
Rami Abdurrahman, who heads the Britain-based Syrian Observatory for Human Rights, said Syrian government forces have captured some 10 neighborhoods over the past few days, putting nearly 30 percent of Aleppo's formerly rebel-held neighborhoods under state control.
Government forces captured the Hanano district on Saturday, the first time they had pushed this far into eastern Aleppo since 2012.
Thousands of east Aleppo residents have fled to safety in government and Kurdish-controlled areas of the city since Saturday.
State TV said 3,000 people, half of them children, have fled over the past few hours. It showed men, women and children in green buses being taken to government-controlled areas.
"It is stinging cold, food is scarce and people are shaken in the streets," Mohammad Zein Khandaqani, a member of the Medical Council in Aleppo, told The Associated Press in a voice text message from east Aleppo.
He added that some residents are taking refuge in mosques while others moved to homes of displaced people in safer areas.
He said although thousands of people have fled to government or Kurdish-controlled areas in Aleppo, many stayed because they are wanted by the state.
The Russian Defense Ministry also said Syrian government troops had pushed the rebels from Qadisia which it described as the "key neighborhood of eastern Aleppo."