A car bomb struck an upscale area of Damascus on Friday, near the central law courts and ministry of information, state TV reported just two hours after a first bomb attack in the north of the capital.
"A terrorist car bomb attack hit the Mazzeh area (west of Damascus), in a street between the justice palace and the ministry of information," the state broadcaster said.
The central Damascus explosion only caused material damage to several cars in the area, the report said.
The Britain-based Syrian Observatory for Human Rights also reported a car bomb blast near the central law courts.
The earlier blast, a motorcycle bomb, struck in the northern district of Rukn al-Din, killing at least five members of the security forces, according to state television.
The bomb exploded as worshippers left a mosque after Friday prayers in the area. "The terrorist attack killed five members of the security forces and injured several others," the television report said.
The Observatory also said that at least five soldiers were killed, and at least six others were wounded.
Anti-regime protests have been held in towns and cities across Syria every Friday following weekly Muslim prayers since the March 2011 outbreak of an uprising against President Bashar al-Assad.
On Friday protests were held under the slogan of "Besieged Homs is calling us," a reference to the central Syrian city which has been under army siege for several months.
Assad's regime has blamed "armed terrorist groups" backed by the West and several Gulf countries for violence in Syria.