"Three mortar shells fired by terrorists landed... in the Qassaa district, killing eight civilians and wounding 24 others," SANA news agency reports.
A fourth mortar was targeted at the Holy Cross church in the neighbourhood.
This is one of the biggest Greek Orthodox churches in Syria.
The shells were fired from the outskirts of Damascus, where rebels have set up a series of rear bases.
Last month, a woman was killed by a mortar round which struck the Iraqi consulate in Damascus.