The Syrian Observatory for Human Rights also reported that regime forces on Sunday pounded the town of Tal Abyad in the northern province of Raqa, which sits on the border with Turkey and is held by the rebels.
Turkey had on Friday shelled a Syrian military position south of Tal Abyad in retaliation after a Syrian shell landed on its territory near the border.
That followed heavy bombardments of Syrian military positions near the border since Wednesday, when a shell smashed into a Turkish town killing five civilians and sparking outrage in Ankara and a UN Security Council condemnation.
Sunday's bombardments in Aleppo, where fighting has raged since mid-July, targeted the embattled district of Sakhur in the east and Kalasseh in the southwest, the Britain-based Observatory said.
Fierce battles broke out between troops in rebels in Sakhur, further east in Hanano and in the central district of Midan, the watchdog added.
A military source told an AFP correspondent that there were overnight clashes near the historic Umayyad Mosque and that the army repelled an attempt by rebels to take a nearby street.
In Damascus province, the bodies of 10 men, at least one of them a rebel fighter, were found after several days of military operations in the town of Hameh that ended in the government taking control, the Observatory said.
Syrian state television said "Hameh and Qudsaya in Damascus province have been cleansed from the armed terrorists," using the regime's blanket term for the rebels.
The latest violence followed a bloody day on Saturday in which 154 people - 47 civilians, 62 troops and 45 rebels were killed nationwide, according to the Observatory, which gathers its data from a network of activists, medics and lawyers on the ground.
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