The opposition-linked group said artillery hit the district of Arqab 3 miles (5 km) from the Opera House.
Fighting continued all night and into Monday around the capital as well as in the northern provinces of Idlib and Aleppo it said.
Damascus residents said the speech was met with celebratory gunfire in pro-Assad neighbourhoods.
But even there some saw no sign peace was any closer although the cabinet was due to begin implementing the plan to "solve the crisis in Syria".
A loyalist resident of southern Damascus who gave only her first name Aliaa said the speech was eloquent but empty.
"It sounded more like gloating than making promises " she said. "I agree with the ideas but words are really just words until he takes some action. He needs to do something.
In the once-affluent district of Mezzeh scene of several bomb attacks an Assad critic said people had more pressing concerns. "Here no one cares about this speech. They care about food and electricity."
Another said few had watched the speech and that Assad’s crackdown would not stop.