The car bombs exploded shortly after 6.40 a.m. (0440 GMT) in the eastern district of Jaramana, home to many of Syria's Druze minority as well as Christians who have fled violence elsewhere.
State news agency SANA described the blasts as "terrorist bombings", a label it reserves for the mainly Sunni Muslim rebel fighters who have been battling to overthrow Assad, a member of Syria's Alawite minority which is linked to Shi'ite Islam.
SANA said the car bombs caused serious damage as well as deaths and injuries. Two smaller bombs also exploded in Jaramana at around the same time.
Addounia television broadcast footage of firefighters hosing down the blackened hulks of two vehicles. Debris from neighbouring buildings had also crushed several other cars.
The television channel quoted a reporter on the scene as saying at least 34 people had been killed. The Syrian Observatory for Human Rights, an opposition group which has monitored the violence throughout Syria's 20-month-old uprising, said 34 people were killed and dozens wounded.
It said 10 bags containing the remains of unidentified victims had also been collected. Eighty-three people were seriously wounded, it said.