The offensive comes the same day that UN peace envoy Staffan de Mistura is to address the Security Council on his efforts, including a plan to "freeze" fighting in Aleppo that has so far failed to gain traction.
A Syrian military source said government troops had seized two villages north of Aleppo and were engaged in fierce fighting for control of a third.
The villages are strategically located by a road that serves as a key supply route for the rebels, leading from the east of Aleppo to the Turkish border.
Nubol and Zahraa have been under rebel siege for more than 18 months, and pro-government militants inside the villages have repelled several attacks.
The Syrian Observatory for Human Rights, a Britain-based monitor, also reported the fighting, saying 24 rebels and 20 regime forces -- among them foreign pro-regime fighters -- had been killed.
"The regime troops have two goals in the area: to cut the road leading from Aleppo to the Turkish border, which is the key supply road for the rebels, and to open the way to Nubol and Zahraa," Observatory director Rami Abdel Rahman said.
The Observatory reported fierce clashes in several parts of the government-controlled west of the city, where at least 11 rebels were killed.
Rebel rocket fire into several western neighbourhoods also killed eight civilians, the monitor said, among them a child.
Once Syria's industrial powerhouse, Aleppo has been split between rebel control in the east and regime control in the west since shortly after fighting began there in mid-2012.
In the surrounding countryside the situation is largely the reverse, with rebels controlling much of the area west of the city and regime forces much of the east.
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