The Syrian Observatory for Human Rights said another 79 people were wounded in the bombardment by an Islamist rebel brigade.
Several of the wounded were in serious condition, and the death toll was expected to rise, the Observatory said.
Observatory director Rami Abdel Rahman said more than a dozen areas of Damascus had been targeted, including in the upscale western Mazzeh district and central Abu Rummaneh.
Opposition fighters on the outskirts of the city have regularly fired mortar rounds and rockets into Damascus, targeting various neighbourhoods and often causing casualties.
On Sunday, regime strikes on Kfar Batna, east of Damascus, and Douma, northeast of the capital, hit marketplaces and killed at least 64 people, among them at least 11 children, the Observatory said.
More than 170,000 people have been killed in Syria's war since peaceful anti-regime protests in March 2011 became an armed conflict after the government put the demonstrations down with force.
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