Despite condemnation from Washington and the UN, there was little sign that the government advance would be halted.
A week into the latest round of fighting for the city, Syrian troops had taken control of a third of the key eastern neighbourhood of Masaken Hanano, the Syrian Observatory for Human Rights said.
Government troops, backed by Russian and Iranian forces and Lebanon's Shiite Hezbollah group, were battling rebels on several fronts inside opposition-held districts, said Rami Abdel Rahman, the head of the Britain-based Observatory.
The renewed fighting has killed more than 140 civilians in east Aleppo and comes amid international concern for the fate of over 250,000 civilians trapped in besieged rebel-held areas.
But despite condemnation from Washington and the UN, there was little sign that the government advance would be halted.
Recapturing east Aleppo, which rebels seized in 2012, would be the government's biggest victory yet in the conflict and deal a potentially decisive blow to the opposition.
The city was once the country's economic powerhouse, but it has been ravaged by the war that has killed 300,000 people since began with anti-government protests in March 2011.
For the past four years, it has been divided between the government-controlled west and rebel-held east.
Masaken Hanano has been heavily shelled during the war, so many of its residents have long abandoned their homes, but the latest fighting has prompted even the last holdouts to flee.
Milad Shahabi, a member of the local council, told AFP overnight that "civilians started to flee the neighbourhood", heading to southern parts of the rebel-held east.
"We are looking for empty houses to accommodate them," he said.
The neighbourhood is symbolically important, as it was the first district in the city to fall to rebels in 2012, but is also strategically key.
"If they take control of Masaken Hanano, the regime will have line-of-fire control over several rebel-held neighbourhoods and will be able to cut off the northern parts of rebel-held Aleppo from the rest of the opposition-held districts," Abdel Rahman said.
The government advances added to a growing sense of despair in the east of the city, which has been sealed off from the outside world since the army surrounded it in mid-July.
No food aid has entered since then, prompting food and fuel shortages, and electricity and water supplies are erratic.
Rebels have tried several times to break the siege on the east, without success, and one European diplomat said it seemed only a matter of time before the city fell to government forces.
"Now, it's just a question of how long they (rebel forces) can hold on," the diplomat said, speaking on condition of anonymity.
"There is nothing to eat, no more hospitals and the bombardment is non-stop. They are under very strong pressure."
The Observatory says 141 civilians, including 18 children, have been killed in east Aleppo since the latest assault began on November 15.
Another 16 civilians, including 10 children, have been killed in rebel fire on western Aleppo, the monitor says.
The regime assault has prompted international criticism, with France's UN ambassador Francois Delattre accusing Damascus of a "total-war strategy".
"The situation is horrific, catastrophic," he said Monday.
The UN's aid chief Stephen O'Brien slammed the use of sieges in Aleppo and elsewhere in remarks to the Security Council on Monday, saying nearly one million Syrians were living under blockades.
"Civilians are being isolated, starved, bombed, denied medical attention and humanitarian assistance in order to force them to submit or flee," he said.
The UN's Syria envoy Staffan de Mistura was in Damascus over the weekend to discuss a humanitarian plan and a truce proposal for Aleppo, but both were rejected by the government.
The humanitarian plan seeks to evacuate the sick and wounded from the east, as well as deliver aid and allow doctors to enter.
The truce plans calls for the departure of jihadist fighters from the east, but would allow the opposition administration there to remain, at least temporarily.
Syria's Foreign Minister Walid Muallem said Sunday the truce plan would "reward terrorists", and insisted that the government would recapture the east.