"Twelve citizens were killed and 50 others wounded by terrorists who targeted the Shaghour neighbourhood in Damascus with four mortar shells," the SANA news agency said, adding that two shells hit the Badr al-Din al-Hussein technical institute.
The Syrian government and media use the term "terrorists" for all those seeking to overthrow President Bashar al-Assad's government.
The Syrian Observatory for Human Rights also reported the mortar attack, saying at least eight people were dead and dozens injured and the toll was expected to rise.
Shaghour is a district in the Old City of Damascus, which has been hit by rebel fire frequently.