"Militants in the Jobar quarter launched more than 30 missiles targeting the Bab Tuma and Kassaa quarters. The death toll has risen to five and more than 30 were injured," the source said.
The borough of Bab Tuma is part of the Old City, filled with historical sites.
On January 4, anti-government Syrian militants fired a mortar round into the historical center of Damascus. The shell fell in the residential quarter of Al-Amar; a woman was killed and 22 more people were injured.
On December 31, one civilian was killed and another one was injured in the suburbs of Damascus in a shelling.