A mortar round slammed into a mainly-Christian sector of Damascus on Wednesday, killing two people and wounding seven, the official SANA news agency said, citing police.
The report, using the regime's term for rebels, blamed "terrorists" for the attack on the Bab Tuma neighbourhood in the centre of the Syrian capital.
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Another shell smashed into the Al-Hal market in Zablatani neighbourhood, also in the centre of Damascus, wounding 13 people and causing damage to shops, SANA said.
The Syrian Observatory for Human Rights monitoring group reported three people killed and 30 wounded by mortar fire in the two neighbourhoods on Wednesday.
Government-held districts of central Damascus have come under repeated bombardment in recent months from rebel positions on the outskirts of the capital that repeated assaults by the army have failed to eliminate.
On Tuesday, at least 16 people were injured by mortar fire while on Monday nine children were killed and more than 20 wounded in two districts of Damascus, state media reported.