State TV footage of the blasts showed massive destruction in the al-Qazzaz suburb to the south of Damascus said to house a military intelligence complex.
The TV report said they were "terrorist bombings". Damascus has been the target of several bombs in past months amid continuing anti-government unrest.
The two sides are supposed to observe a ceasefire monitored by UN observers.
But violence has continued unabated, with the restive city of Homs shelled again overnight.
The UN and Arab League Special Envoy on Syria, Kofi Annan, has condemned the Damascus blasts as "abhorrent", saying they were counter-productive to the interests of all parties.