A car bomb exploded outside a police station in a Christian quarter of Damascus on Sunday, killing 13 people, the official SANA news agency said, while a similar attack struck Syria's second city of Aleppo.
"An explosive device planted under a car in Bab Tuma exploded, killing 13 people and wounding 29," said SANA, blaming an "armed terrorist group," the regime's term for rebels.
The Syrian Observatory for Human Rights said 10 people were killed and 15 others wounded when "a car bomb exploded in Bab Tuma Square in front of the police station" in the capital's Old City.
It did not specify if the casualties were police or civilians.
State television said significant material damage was caused by the blast and it showed mangled cars and debris littered on the ground.
It was the first such attack in Bab Tuma, one of the oldest quarters of the capital, since an anti-regime revolt broke out in March 2011, costing 34,000 lives nationwide, according to the Observatory.
A large part of Syria's Christian community backs President Bashar al-Assad, fearful of the influence of Islamists in the revolt.
One resident told AFP by telephone that the car blew up in a parking lot in front of the police station. "My house a kilometre (less than a mile) away shook" from the force of the blast, another said.
SANA also reported that a number of "terrorists" were killed when a bomb they had planted by a mosque in the Assali district of southern Damascus exploded prematurely.
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The Observatory reported fierce clashes between the army and rebels in Assali, and that the bodies of two men were found shot dead in the nearby neighbourhood of Qaboon.
In the town of Harasta, northeast of the capital, nine people, including a child and three rebels, were killed in clashes and shelling, said the watchdog, which also reported bombardment of the nearby town of Irbin.
Elsewhere, nine soldiers were killed and wounded in a roadside bombing near Al-Tal, a town just north of Damascus.
In Aleppo, a car bomb exploded in the Sarian district, leaving body parts scattered, wounding several people, an AFP correspondent said. A security source said the blast was caused by "a suicide car bomber."
Also in the northern city, fierce clashes broke out between rebels and troops around the ancient Citadel, the Observatory said, adding that four rebels were killed in fighting across the city.
According to the AFP correspondent, Internet connections in Aleppo and other areas in the largely rebel-held north of the country were down since early Saturday, while mobile connections were unreliable.
The Observatory also said that regime forces stormed the rebel town of Artuz, "burning" homes while heavy bombing also continued over the northwestern town of Zabadani near the border with Lebanon.
Renewed fighting was reported at the southern entrance to Maaret al-Numan, a strategic town on the Aleppo-Damascus highway that fell under rebel control on October 9, blocking off a key army supply route.
The Observatory gave an initial toll of 55 killed across the country on Sunday: 19 civilians, 25 soldiers and 11 rebels.