State news agency SANA said on November 26 that Syrian forces were now in "full control" of the Hanano district and were clearing the area of mines and bombs.
It said eight civilians were killed in the air-strikes and shelling by Government forces.
Global pressure resulted in aid reaching the rebel-held town of Madaya and Shia towns of Kefraya and Foua earlier this year after evidence of mass starvation emerged but many other areas remain cut off by fighting and in desperate need.
But with many residents of eastern Aleppo sympathetic to the opposition and deeply distrustful of Assad, there has been no sign of major unrest targeted at rebel fighters.
The UN says it has a plan to deliver aid to Aleppo and evacuate the sick and wounded, which rebel factions have approved.
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Trump, who takes office on January 20, has been interviewing candidates for his Cabinet and other top White House positions. Carrier also cited an agreement it had reached with the United Steelworkers union about compensation for affected workers.
The Observatory said the army now controlled more than 60 percent of the strategic Masaken Hanano district and was pushing on.
The Syrian Observatory for Human Rights, which relies on a network of activists on ground, said the Syrian forces were making rapid progress in eastern Aleppo, where over 250,000 civilians are trapped.
The city has been divided since 2012 between the rebels in the eastern part of the city and the government forces in the west.
But he said Canada is a respected country, and asked that it also mount a diplomatic push with other countries to help the World Food Program regain access to besieged Syrians. Government forces said they are in "full control" of the district and were working to clear it of landmines and improvised explosive devices.
Yasser al-Yousef, from the political office of the Nour al-Din al-Zinki rebel group, said insurgents had been fighting fiercely for the past 48 hours to defend Hanano and the southern front of east Aleppo from heavy government bombardment. "We can barely get one bottle of powdered milk a month", said Abdullah Hanbali, who worked as an engineer before the war.
Syrian air force hit main children's hospital in Aleppo
Since then, hundreds of thousands of people are believed to have been killed and millions more displaced by the conflict. At least one paramedic was among the dead, according to the Syrian Civil Defense.
Damascus says east Aleppo residents and surrendering fighters are free to leave but accuses the rebels of using civilians as "human shields". "At first they were afraid but when they saw many people around and that there was no bombardment they were reassured", he said.
An official from Jabha Shamiya, one of the biggest groups fighting against Assad in northern Syria which has some fighters in Hanano, said there are back-and-forth battles and about half of Hanano has been taken by the government.
More than 250,000 civilians have been besieged in eastern Aleppo since July, with food and fuel supplies dwindling and worldwide aid exhausted.
Retaliatory rocket fire by the rebels has killed at least 18 civilians in the government-held west, 10 of them children, since the regime assault began on November 15, said the Observatory. It said hundreds of fighters from both suburbs will be evacuated to the northwestern province of Idlib, a rebel stronghold.
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