Syrian state media said an explosion hit the district of Hai al-Wuroud, in the northwest of the capital, and that an "initial tally" indicated ten people were killed and 30 wounded.
Activists said three bomb explosions were heard and smoke was seen rising from the area in the latest tit-for-tat attack. The hilltop neighbourhood is situated near a barracks and housing for elite army units.
Earlier on Tuesday state television reported that the brother of Syria's parliament speaker had been assassinated by gunmen in Damascus, the latest victim in a campaign against perceived Assad supporters and their families.
A bomb attack on Monday in the western "Mezzeh 86" district of Damascus killed 11 people and wounded dozens more, Syrian state media reported.
Seif al-Sham, an Islamist rebel unit, claimed responsibility for that attack, which targeted what it described as a meeting point for the army and police, as well as the shabbiha (ghost) militia loyal to Assad.
Damascus has several hilltop enclaves mostly inhabited by members of the Alawite minority, an offshoot of Shi'ite Islam that has dominated Syria since the 1960s. Syria's rebellion draws most of its support from the Sunni Muslim majority.
"After bomb attacks and constant ground aerial bombardment on Sunni districts, it seems Alawite areas are now considered fair game," Nawara al-Soueid, an opposition activist in the capital, said.
Last month several bombs exploded during the Muslim Eid holiday near mosques in Sunni districts and the Damascus suburbs, killing or injuring dozens of people, activists said.
