"Terrorists who call themselves Jaish al-Islam (Army of Islam) this morning fired a mortar round into the residential district of Barzeh (north of Damascus), killing one civilian and wounding nine people," it said, citing police.
Rebels battling President Bashar al-Assad's regime often shell the capital from the suburb of Eastern Ghouta.
SANA also said that in second city Aleppo in the north, "rockets fired by terrorists hit a residential district, killing three girls and wounding another two".
The Observatory, which has an extensive network of informants inside Syria, also said several people were wounded by rocket fire on the regime-controlled Aleppo neighbourhood of Hamdaniyeh.
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Syria's former economic powerhouse has been ravaged by war since 2012. It is split between the government-held west and insurgent-controlled east.
Aleppo province itself is almost entirely under the control of Syria's Al-Qaeda affiliate, Al-Nusra Front, jihadist forces allied to it and the Islamic State jihadist group.
Elsewhere, SANA said, "terrorists targeted the town of Suqaylabiyah (northwest of the central city of Hama) with rockets, causing the death of two civilians and wounding eight, including a child."
More than 250,000 people have been killed in Syria since the conflict broke out nearly five years ago, and millions more have been displaced.