The bomb killed 11 people and wounded 40 at a station packed with Syrians queuing for fuel, which has become scarce in the 21-month insurgency against Assad, in the second petrol station attack in the capital this week, opposition activists said.
"Terrorists ... blew up an explosive device at Qassioun Petrol Station near Hamish Hospital in Barzeh, Damascus, martyring several civilians," state news agency SANA said.
The United Nations says more than 60,000 people have been killed in the civil war, the longest, bloodiest conflict born from uprisings across the Arab world in the past two years.
Dozens of people were incinerated in an air strike as they waited for fuel at another Damascus petrol station on Wednesday, according to opposition sources.
The semi-official al-Ikhbariya television station aired its own footage from Barzeh, indicating the attack struck a government-held area. Barzeh's residents include members of the Sunni Muslim majority and religious and ethnic minorities.
The rebels hold a crescent of suburbs on the southern and eastern edges of Damascus, which have come under bombardment by government forces. Rebel forces also seized territory in Syria's north and east during advances in the second half of 2012.
The war pits rebels, mainly from the Sunni Muslim majority, against a government supported by members of Assad's Shi'ite-derived Alawite sect and some members of other minorities who fear revenge if he falls. Assad's family has ruled for 42 years since his father seized power in a coup.
Fighting has forced 560,000 Syrians to flee to neighboring countries, according to the U.N.
Lebanon, a country which has so far tried to distance itself from the conflict next door for fear it will inflame sectarian tensions, approved a plan to start registering 170,000 Syrian refugees and ask international donors for $180 million in aid.
"The Lebanese state will register the refugees...and guarantee aid and protection for the actual refugees in Lebanon," Social Affairs Minister Wael Abu Faour said after a six-hour cabinet session on Thursday night.
A Lebanese citizen who crossed into Syria through a mountainous frontier region said the army appeared to have withdrawn from several border posts and villages in the area.
Rebels controlled a line of border towns and villages north of the capital Damascus, stretching about 40 km (25 miles) from Yabroud south to Rankus, said the man, who did not want to be named and visited Syria on Wednesday and Thursday.
Rebels in the area reported that some of Assad's forces have pulled back to defend the main north-south highway linking Syria's main cities of Damascus, Homs, Hama and Aleppo, while others were sent to reinforce the northern approach to Damascus.
"The border is controlled by the Free Syrian Army rebels," he said on Friday, adding he had crossed through mountainous terrain, covered in parts by more than a meter of snow.