On Saturday, air raids hit the town of Zamalka to the east, Douma to the northeast, and there were multiple strikes on the Eastern Ghuta region that runs along the eastern belt of the capital, Damascus, the Syrian Observatory for Human Rights said.
Warplanes also raided the town of Sabineh just south of Damascus, alongside the highway that leads to Daraa province and the town of Moadamiyet Al-Sham to the southwest.
Fierce clashes broke out between rebels and troops in the embattled town of Daraya, as the army shelled insurgent positions there, the Observatory said. Fighting also raged in the eastern Jobar district after a heavy explosion was heard overnight in Rokn Eddin in the north, where rebels reportedly attacked an army checkpoint.
The latest clashes come after the army launched this week a major offensive against rebel zones surrounding the capital in an effort to break a stalemate in the two-year uprising against President Bashar Al-Assad's regime.
Pro-regime newspaper Al-Watan said the army was "determined to crush terrorism around the capital and in big cities."
Elsewhere Saturday, a child was killed in shelling on the city of Qusayr in the central province of Homs, which has been under daily bombardment for a year.
In Homs city, where hundreds of civilians have been trapped for months by an army siege against rebel-held districts, troops renewed shelling attacks on those areas, the UK-based Observatory said.
Clashes also broke out in the eastern city of Deir Ezzor and in the southern province of Daraa.
The Observatory, which gathers its information from a network of medics and activists, reported 136 deaths in Friday's violence, including 56 civilians and five Kurdish fighters killed fighting against the army in the northern city of Aleppo.
A UN figure puts the number of people killed in Syria's conflict at more than 60,000.