Similar clashes also reportedly took place near Rijeh Square close to the Palestinian camp.
Earlier in the day, foreign-sponsored militants raided an army roadblock near al-Khalsa neighborhood in the capital.
The clashes came while diplomatic efforts are under way to end the Arab country’s months-long crisis.
The UN-Arab League Special Envoy to Syria Lakhdar Brahimi arrived in Syria on Sunday on his third visit to Damascus since he was appointed to his current position in August.
On Tuesday, Brahimi met with Syrian opposition groups who called for a political solution as the only way to end the unrest in Syria and expressed strong opposition to any foreign military intervention.
The veteran Algerian diplomat also met with President Bashar al-Assad in the capital on Monday, saying the two discussed the “many steps to be taken in the future” on how to resolve the unrest in Syria.
Syria has been experiencing unrest since March 2011. Many people, including large numbers of security forces, have been killed in the turmoil.
The Syrian government says the chaos is being orchestrated from outside the country, and there are reports that a very large number of the militants are foreign nationals.