The explosions struck the eastern neighborhood of Jaramana, home to many of Syria's Druze minority as well as Christians who have fled violence elsewhere, ripping through nearby shops and bringing debris crashing down on cars.
Car bombs have shaken Damascus - once a bastion of security in Assad's 20-month campaign to crush an uprising against his rule - with growing regularity but Wednesday's attacks were the deadliest in the capital for several months.
Authorities severely limit independent media in Syria and it was not immediately possible to verify reports. The government said 34 people were killed.
The bombs followed two weeks of military gains by rebels who have stormed and taken army bases across Syria, exposing Assad's loss of control in northern and eastern regions despite the devastating air power which he has used to bombard opposition strongholds.
Underlining the growing military muscle of the rebels, bolstered by weapons captured during raids on army facilities as well as supplies from abroad, fighters shot down a war plane in the northern province of Aleppo on Wednesday using an anti-aircraft missile, the Syrian Observatory for Human Rights said.
Opposition group subsequently posted a video clip on the Internet that showed a man in a green jumpsuit being carried through fields. He was bleeding heavily from his head and appeared unconscious; "This is the pilot that attacked the houses of civilians," said a voice off camera.
Another video showed a blackened and smouldering tail fin of what activists said was a MiG-23 warplane.
The bloodshed came as Syria's new opposition coalition held its first full meeting on Wednesday in Cairo to discuss forming a transitional government crucial to win effective Arab and Western support for the revolt against Assad.
"The objective is to name the prime minister for a transitional government, or at least have a list of candidates," said Suhair al-Atassi, one of the coalition's two vice-presidents.
The two-day meeting will also select committees to manage aid and communications, a process that is becoming a power struggle between the Muslim Brotherhood and secular members.
Rivalries have also intensified between the opposition in exile and rebels on the ground in Syria, where the death toll has reached 40,000, including soldiers, civilians and rebels.'Terrorist' bombs
State news agency SANA described Wednesday's blasts as "terrorist bombings", a label it reserves for attacks by mainly Sunni Muslim fighters battling to overthrow Assad, a member of Syria's Alawite minority linked to Shiite Islam.
Two smaller bombs also exploded in Jaramana at about the same time as the car bombs, around 7 a.m. In total at least 47 people were killed, the Syrian Observatory for Human Rights said. Eighty three people were seriously wounded.
"Who benefits from this? Tell me who benefits from this? America, Israel, Qatar?" a man at the bomb site said to Syrian television, which broadcast footage of firefighters hosing down the blackened hulks of two vehicles and several cars crushed by debris from neighboring buildings.
Pools of blood could be seen on the road.
Activists also reported air strikes on the town of Maarat al-Numan, a rebel-held town near the main north-south highway linking Damascus with Syria's largest city, Aleppo.
Rebels around Maarat al-Numan have been trying for weeks to dislodge Assad's forces from the military base of Wadi al-Deif, a few hundred meters from the highway.
Most foreign powers have condemned Assad. Britain, France and Gulf countries have recognized the umbrella opposition group meeting in Cairo, the Syrian National Coalition, as the sole representative of the Syrian people.
But Assad has been able to rely on his allies, especially regional powerhouse Iran, which is believed to be bank-rolling him and supplying military support despite US and European sanctions. Russia, Syria's main arms supplier, says it has only sent weapons already agreed to in previous deals.
International Syria mediator Lakhdar Brahimi is due to brief the 15-member council on Thursday and the UN General Assembly on Friday. There is diplomatic deadlock between Western powers, who broadly support the opposition and Assad's supporters Russia and China which have blocked Security Council action.
French Foreign Minister Laurent Fabius, speaking after a visit to Paris by Russia's Prime Minister Dmitry Medvedev, said he had not given up hope of forging a united position.
"If we want to avoid the country being torn apart completely, then we need to bring the Russians back on board," Fabius told France Inter radio.
"We must not end up with an Iraqi scenario whereby after Bashar, there is nothing left except jihadis. We are trying to build ... an alternative to Bashar and we hope the Russians will end up understanding this."
BEIRUT (Reuters) -- Two car bombs exploded in an attack that killed at least 34 people on Wednesday in a district of the Syrian capital loyal to President Bashar Assad.