Reports said government troops had recaptured two military academy sites in the south of the city and severed a recently-established rebel supply line.
The government offensive was backed by Syrian and Russian air strikes.
There are about 250,000 civilians living in the city's rebel-held areas.
UK-based monitoring group the Syrian Observatory for Human Rights confirmed that government troops had retaken the Armaments Academy and Air Force Technical College.
"The army took control of the artillery academy, so they control all the academies, and the eastern neighbourhoods are under a full siege," said Rami Abdel Rahman, director of the Observatory.
Syrian state media also reported on the advance and recapture of the military academies.
Meanwhile, US President Barack Obama said on Sunday that the US and Russia were struggling to reach a ceasefire agreement on Syria.
Speaking to reporters at the G20 meeting in China, Mr Obama said: "We have grave differences with the Russians in terms of both the parties we support but also the process that is required to bring about peace in Syria."
Aleppo: Is besieged Syrian city facing last gasp?
The story of Syria's bitter conflict
Aleppo has been divided by the country's bitter civil war, with various rebel groups controlling parts of the east of the city and pro-government forces the west.
Pro-government forces slowly surrounded the city and in July cut off access to rebel-held areas.
The brief supply line established by rebel advances early last month allowed some goods into the area but aid agencies have been unable to reach the population.
Operating with support from Russia and Iran, Syrian President Bashar al-Assad intends to recapture all of Aleppo from the rebel fighters.
Syrian government forces have recaptured parts of Aleppo city which were lost to rebels last month, placing rebel-held districts in the city's east once again under siege, monitors said.