Mortar shells landed in Damascus University on Thursday, killing at least 12 people, dpa reported according to state-run television.
It blamed the attack on "terrorists," a term used by the government to refer to rebels fighting overthrow President Bashar al-Assad.
The Britain-based Syrian Observatory for Human Rights activist group said eight people were killed in the attack
The watchdog added that government troops shelled pro-rebel areas near Damascus and clashed with militants.
Opposition forces have stepped up attacks in and around Damascus, raising the possibility that al-Assad could lose hold on the capital.
At least 70,000 people have been killed in Syria's two-year conflict, according to the United Nations.