In the first advance since announcing plans last week to retake all of the divided city, pro-government troops seized the Farafina district northwest of Aleppo's historic citadel, a military source told AFP.
"After neutralising many terrorists... Units are now demining the area," the source said.
The push follows several days of Syrian and Russian air strikes on rebel-held Aleppo neighbourhoods - some of the fiercest bombardment of the five-year conflict so far - after a ceasefire deal brokered by Moscow and Washington collapsed last week.
In the latest broadside, NATO Secretary General Jens Stoltenberg also condemned the air campaign.
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"The appalling attacks on Aleppo have shaken all of us, and the violence and the attacks we have seen... Is morally totally unacceptable and is a blatant violation of international law," Stoltenberg told a news conference in Bratislava.
On the ground in eastern Aleppo, an AFP correspondent said air strikes struck several neighbourhoods simultaneously, including in Al-Shaar, where a five-storey building was levelled with a family stuck inside.
The Syrian Observatory for Human Rights, a monitor, said that more than 155 people have been killed by Russian and regime bombardment on Aleppo city since the government announced its offensive last week.
They include 11 civilians killed today in raids on the neighbourhoods of Al-Shaar and Al-Mashhad, according to the Britain-based group.
As well as the intensified violence, residents have been left reeling from food shortages and skyrocketing prices.
"Over the last weekend alone, more than 200 people were injured and taken to understaffed health facilities in east Aleppo," a spokeswoman said in Geneva.
The UN body called for "an immediate establishment of humanitarian routes to evacuate sick and wounded from the eastern part of the city.