The earlier explosions in Damascus happened close to Omayyad Square, in the heart of the capital.
State TV says the attack was on a military checkpoint close to the army and air force headquarters.
The office of Syria's Vice-President Farook al-Shara'a is also in the area. The blast happened just hours after a reported 15 people were killed in a car bomb attack on Saturday in Sbeneh, a relatively poorer neighbourhood in southern Damascus.
Al Jazeera's Sue Turton reports from Antakya, Turkey.