Syrian troops backed by helicopter gunships clashed with rebels near an army barracks in Aleppo, according to the Syrian Observatory for Human Rights (SOHR).
Fighting erupted overnight near the Hanano barracks in the Arkoub district of northeast Aleppo on Friday, the UK-based watchdog group said.
Several districts of Aleppo, including Sakhur in the northeast and Bustan al-Qasr in the centre, came under overnight attack, SOHR said.
Elsewhere in Aleppo, fighting broke out between troops and rebels near the Meng military airport, SOHR said.
Military airports have been a key target for the rebels as the army has increasingly deployed fighter jets and helicopter gunships to launch devastating attacks against them.
In-depth coverage of escalating violence across Syria
SOHR further reported a massive explosion, believed to be a car bomb, northwest of Damascus. Heavy gunfire was heard afterwards but there were no immediate reports of casualties, it said.
In the central province of Homs, a civilian was killed in dawn shelling of Rastan, while the eastern city of Deir Az-Zor and the town of Daal, in the southern province of Deraa, also came under bombardment.
The violence across the country came a day after dozens of people were killed when an air raid hit a fuel station in the northern province of al-Riqqa on Thursday.
Al Jazeera's Andrew Simmons, reporting from Antakya in neighbouring Turkey on Friday, said there is "no doubt that it was a targeted attack on an area being used by civilians".
"The petrol station was crowded with vehicles," he said. "It was the only petrol station in the entire region that was open to the public, according to activists.
"It was supposed to be an improvised device; we are hearing from unconfirmed reports [it was] a barrel bomb. These sorts of things have been described in Aleppo before. It was devastating.
"The casualties number in the dozens, and now we are getting unconfirmed reports that the death toll has reached 60."
'Friends of Syria'
In the interview to Al-Ahram al-Araby, Assad said he was neither optimistic nor pessimistic about the Brahimi mission.
Lakhdar Brahimi, the joint UN-Arab League negotiatior, who met Assad last week in Damascus, said his visit confirmed that the situation was "extremely dangerous and escalating".
"I welcome dialogue with the national opposition but those who choose arms have put themselves in confrontation with the Syrian Arab army," Assad told Al-Ahram al-Araby.
He also admitted there was corruption and mistakes had been made.
In another development, diplomats from more than 60 nations and the Arab League met in The Hague, Netherlands, on Thursday to toughen and improve co-ordination of sanctions against Assad's regime.
"We need vigorous implementation," Uri Rosenthal, Netherlands foreign minister, told the opening of the Friends of Syria working group.
"Sanctions will only have an impact if they are carried out effectively. That is how we can make a difference."
The Friends of Syria group has already held three meetings at ministerial level in Tunis, Istanbul and Paris. Another is planned in Morocco in October and another later in Italy.