A bomb killed at least two people on Sunday in a neighbourhood of central Damascus that is mainly home to members of President Bashar al-Assad's Alawite minority, a monitoring group said.

State news agency SANA gave a higher toll of three dead, including a three-year-old child.

"The blast that shook the Mazzeh 86 area of Damascus, home to an Alawite majority, was produced by an explosive device planted in a vehicle," the Syrian Observatory for Human Rights said.

"At least two people were killed."

SANA said three people, including the child, were killed and seven people wounded in what it said was a car bombing.

It was the third bombing to hit the capital on Sunday.

Earlier, bombs hit a police station in Rukn al-Din in north Damascus and a security branch in Bab Musalla in the southwest, killing at least eight people, according to the Observatory.

The interior ministry said 11 people died, six of them "terrorists", in the two attacks.

The violence came as the army kept up an offensive aimed at ousting rebels from footholds on the outskirts of the capital that they have used as launchpads for attacks.