The TV report does not give exact numbers of deaths, saying only "a number of military personnel and civilians, mostly civilians," died.
Media reports said the explosions were caused by car bombs and happened in the Kfar Sousa district of the capital close to a complex housing security and intelligence services.
State TV suggested the blasts could be the work of al Qaeda-linked militants.
The Syrian state has blamed terrorists and foreign interference for the ongoing protests against President Bashar al Assad.
The explosions, the first of their kind since the anti-government demonstrations began, come a day after Arab League representatives arrived in Syria to monitor Mr Assad's pledge to end the violence. Read More