ALEPPO — Syrian government forces and their allies clashed with rebels in southeast Aleppo on Wednesday, a rebel official and a monitor said, as Damascus and its allies try to build on major gains in the city.

There were conflicting accounts of the fighting in Sheikh Saeed, on the southeastern edge of Aleppo. A Syrian military source said government troops and their allies had captured the entire district, but a rebel official denied this.

On Wednesday, Syrian rebels vowed to fight on in the face of sudden government advances that have cut the area held by the opposition by a third in recent days and brought insurgents in the city to the brink of a catastrophic defeat.

Gains by the Syrian army and its allies since last week have brought whole districts back under government control and led to an exodus as thousands have fled their pulverized neighborhoods near the rapidly shifting front lines.

The army and its allies said they had taken the Sheikh Saeed district in the south of the city on Wednesday. Rebels denied this, saying the government’s advance had been repelled. The Syrian Observatory for Human Rights, a British-based monitoring group, said the insurgents retained a third of Sheikh Saeed, while government forces and allied militias had advanced and seized the rest of it.

Fierce fighting continued in the district, the Observatory said.

Rescue workers in the rebel zone said renewed artillery bombardment had killed more than 45 people, mostly women and children, on Wednesday and injured dozens more, including some of those who had fled from frontline areas. The Observatory put the toll from that attack at 26.