An airstrike Tuesday blamed by activists on the government killed 25 civilians in the same area.
Around 20,000 people have fled the violence in eastern Aleppo in recent days, United Nations humanitarian chief Stephen O'Brien told CNN on Tuesday night.
He said "250,000 civilians living in Aleppo could be killed".
The Russian Foreign Ministry complained on Wednesday that the issue of humanitarian aid in Syria was becoming increasingly politicized and said most United Nations help was going to areas controlled by anti-government rebels.
Syrian state media also reported that eight people, two of them children, had been killed in government-controlled districts by rebel rocket fire.
Eastern Aleppo has been a stronghold for rebel forces in the region for years.
The government has seized much of the northern half of the enclave in a swift advance that began Saturday.
Troops and allied militia have overrun all of Aleppo's northeast and are now chipping away at the far eastern districts of the city, the Syrian Observatory for Human Rights said.
He said there is no properly functioning hospital in eastern Aleppo, which has been under siege for almost 150 days and that most of the almost quarter million people trapped there don't have the means to survive much longer.
A woman and children leave an area of eastern Aleppo after bombardment by government forces. "They send out a cry to the world".
But the BBC's Lyse Doucet in Damascus says the Syrian government and its allies are unlikely to heed calls to halt an offensive it describes as a campaign against terrorism. Thousands of east Aleppo residents have moved to Jub al-Quba and other such neighborhoods fleeing a government advance on the rebel-held east.
In an apparent reference to the opposition groups fighting the regime O'Brien said that "non-state" actors have prevented civilians from leaving, effectively making them human shields.
The Syrian Civil Defense search-and-rescue group operating in eastern Aleppo put the toll at 45 killed.
"Most of their equipment is out of service because of the targeting against their quarters", he added.
More than 50 000 Syrians have joined a growing exodus of terrified civilians from east Aleppo, as the UN Security Council was set for emergency talks on fighting in the city.
Assad has vowed to take all of Aleppo, and regime forces have made rapid progress since entering the east last weekend.
"What we are hoping for is a salvation plan to save the remaining residents of Aleppo", said Yasser al-Yousef, a spokesman for the opposition group Nour el-Din el-Zinki. The general also said that the humanitarian situation in the city districts cleared of militants was very hard, people were without water and electricity. Rebels said that the regime's advance had been repelled. The group posted a video of the captured fighter.