UN chief Ban Ki-moon voiced alarm at reports of atrocities against civilians in Aleppo, where entire districts are in ruins and unclaimed bodies lie in the streets.
Forces loyal to President Bashar al-Assad have said the battle for the city is in its "final phase" after they seized more than 90 percent of the eastern districts which had been held by the rebels since 2012.
The turnaround in the government's fortunes has come through decisive support from its allies Iran and Russia, which has waged a bombing campaign in support of Assad since September last year.
"The regime is combing the districts of Bustan al-Qasr, Kalasseh, Fardaws, and other neighbourhoods it seized yesterday (Monday)," Observatory head Rami Abdel Rahman told AFP.
More From This Section
He said the regime was consolidating its control over those areas but had not made any fresh advances this morning.
The fall of Aleppo would be the rebel's worst defeat of the civil war and put the government in control of all five of Syria's main cities.
An AFP correspondent in government-held west Aleppo said bombardment was heard overnight but had quietened by morning, when thick fog shrouded the city.
UN chief Ban Ki-moon expressed alarm over reports of atrocities against "a large number of civilians, including women and children" in Aleppo, his spokesman Stephan Dujarric said Monday.
"While stressing that the United Nations is not able to independently verify these reports, the secretary general is conveying his grave concern to the relevant parties."
The east of the city had been under army siege almost continuously since July.
On November 15, the army launched a blistering offensive to retake it with the support of Iran-backed militias.
Rebel fighters withdrew from six residential districts on Monday after government forces overran the key Sheikh Saeed neighbourhood on the city's southeastern outskirts.
The pullout leaves the rebels confined to just a handful of neighbourhoods in the southeast of the city, including Mashhad and part of Sukkari.