According to the Syrian Observatory for Human Rights, the fresh advance puts the government in control of more than 70 percent of the former rebel stronghold in Aleppo's east
"Regime forces took full control of Shaar, Dahret Awad, Juret Awad, Karam al-Beik, and Karam al-Jabal," the Britain-based monitor said on Tuesday.
"The regime is cornering the rebels even further," Observatory head Rami Abdel Rahman told AFP.
Backed by allied militia, Syrian troops have waged a fierce three-week assault on eastern Aleppo, a rebel bastion since 2012.
Their rapid advance has left rebels reeling in their shrinking enclave in southeast Aleppo.
Abdel Rahman told AFP the government could now wage a "war of attrition" on encircled rebel groups.
Syrian state news agency SANA confirmed that Syrian troops overran Shaar and several other districts on Tuesday.
The fall of eastern Aleppo would deal the biggest blow yet to rebel forces since Syria's conflict erupted in March 2011.
The regime's campaign has been met with global outrage, but Damascus and its steadfast ally Moscow have said any ceasefire must include a guarantee that all rebel fighters leave the city.