The Observatory, which relies on a network of anti-regime activists inside Syria, said two car bombs had exploded near security centers in Barzeh, followed by intense clashes between rebels and security forces.
Syrian state media also reported that security forces in Damascus had arrested a second, would-be suicide bomber driving a car full of explosives near the site of the Mazraa bombing.
Damascus has so far mostly avoided the large-scale violence that has destroyed other Syrian cities, though deadly car bombings have targeted government buildings in the capital.
In May 2012, twin car bombs exploded outside a military intelligence building, killing 55 people in the deadliest attack against a regime target in the capital since the uprising began 23 months ago.
And in July, rebels detonated explosives inside a high-level crisis meeting in Damascus that killed four top regime officials, including Assad's brother-in-law and the defense minister.
Following that attack, rebel groups who have established footholds in suburbs of the capital pushed in, clashing with government forces for over a week before being routed and pushed out.
Since then, government jets have heavily bombed rebel-held suburbs and rebels have managed only small incursions on the city's south and east sides.
Syria's conflict began in March 2011 with political protests against the government and has since evolved into a civil war between Assad's regime and hundreds of rebel groups seeking to topple it. The U.N. says some 70,000 people have been killed in the conflict so far.
International diplomacy has failed to slow the fighting.
On Thursday, British Foreign Secretary William Hague said his message to Assad is that "it is time to go."
He said the senseless killing must be brought to an end through a credible political process leading to a transition in Syria.
He also called on Assad to respond to a dialogue offer made recently by Syrian opposition chief Mouaz al-Khatib.
"A political settlement, a political agreement on a transition is the way forward in Syria to bring to an end this terrible and unacceptable loss of life."
Al-Khatib has said he is open to talks with the regime that could pave the way for Assad's departure, but that the Syrian leader must first release tens of thousands of detainees. The government has refused.
Hubbard reported from Beirut. Associated Press writer Zeina Karam contributed reporting from Beirut.
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