The Syrian Observatory for Human Rights said at least 16 Syrian soldiers have been killed in a suicide bombing and fighting that followed in Damascus suburb of Jaramana.
The blast triggered clashes at a checkpoint near the mainly-Christian area of Jaramana, activists say.
State media blamed “terrorists” for the explosion but did not give details.
Earlier, the US urged the Syrian government to allow aid to reach starving civilians in Damascus.
Washington said the army’s months-long siege left many people in rebel-held areas in desperate need of food, water and medicine.
The UK-based Syrian Observatory for Human Rights, which relies on a network of activists inside Syria, said the suicide car bombing by the al-Qaeda-linked Nusra Front triggered heavy fighting at a key checkpoint between Jaramana and the rebel-held town of Mleha.
At least 16 Syrian soldiers have been killed in a suicide bombing and fighting that followed in Damascus suburb of Jaramana
It said rebels fired rockets into Jaramana during the fighting and Syrian fighter jets retaliated by striking nearby opposition-held areas.
The report could not be confirmed.
Rebels control much of the countryside around Damascus but Jaramana – a Christian and Druze area mostly loyal to President Bashar al-Assad – is still held by the government.
In August a car bomb in the suburb killed 18 people.
President Bashar al-Assad has drawn support from Syria’s ethnic and religious minorities, including Christians and members of his Alawite sect, an offshoot of Shia Islam.
The rebel movement is dominated by Sunni Muslims, who are a majority in Syria.
In a statement on Friday, US State Department spokeswoman Jen Psaki said: “We call on the Syrian regime to immediately approve relief convoys.”
And she warned that “those who are responsible for atrocities in the Damascus suburbs and across Syria must be identified and held accountable”.
At least three of Damascus’s suburbs – Yarmouk, Eastern Ghouta and Moudamiyah – have been besieged by government forces for several months.
At least 34 people have been killed and many injured by two car bomb explosions in Jaramana, a south-eastern district of Damascus, Syrian state media report.
State television said “terrorists” were behind the blasts in Jaramana and broadcast pictures showing several charred vehicles and damaged buildings.
The district is predominantly Druze and Christian, two communities which have so far not joined the uprising.
Earlier, there were clashes between security forces and rebels in Jaramana.
There has been fierce fighting in recent days in eastern parts of the countryside around Damascus, known as the Ghouta.
The pro-government TV channel, Addounia, said the car bombs exploded in Jaramana shortly after 06:40 local time.
“Terrorists blew up two car bombs filled with a large amount of explosives in the main square,” the official Sana news agency reported.
State television quoted a source at the interior ministry as saying that 34 people had died and 83 had been seriously injured.
The Syrian Observatory for Human Rights (SOHR), a UK-based activist group, put the death toll at 38.
“Activists and residents in the town said most of the victims were killed when a suicide attacker blew up his car, just after an explosive device was used to blow up another car,” it said.
At least 34 people have been killed and many injured by two car bomb explosions in Jaramana, a south-eastern district of Damascus
Two smaller bombs also exploded in Jaramana at around the same time as the attack, Sana said, adding that nobody was killed by them.
No group has said it was behind the bombings, and there was no immediately obvious military or government target.
“What do they want from Jaramana? The town brings together people from all over Syria and welcomes everybody,” one resident told the AFP news agency.
The population of Jaramana is mainly Christian and Druze, a heterodox offshoot of Islam. It is also home to many Palestinian and Iraqi refugees.
Few members of Syria’s minority groups have supported the revolt against President Bashar al-Assad. They are fearful for their future if the country’s majority Sunni Muslim community chooses an Islamist leadership to replace decades of secular rule.
Supporters of the government in Jaramana and other Damascus suburbs have set up armed vigilante groups – known as Popular Committees – to prevent attacks such as Wednesday’s. On 29 October, 11 people were killed in a car bombing in Jaramana.
Elsewhere on Wednesday, witnesses told AFP that rebel fighters had captured the pilot of a warplane shot down over Darat Izza, in the northern province of Aleppo. One of the agency’s reporters earlier saw a large explosion as the jet crashed near the town.
Fighter jets earlier bombarded rebel positions in the western Damascus suburb of Darayya, the SOHR said.
The government army also reportedly shelled Zabadani, a town in the mountains north-west of the capital. The Syrian Revolution General Commission, an opposition activist network, said more than 50 shells had fallen on the town in 30 minutes, injuring several people.
The Local Co-ordination Committees (LCC), another activist network, reported that at least 50 people had been killed across the country on Wednesday, most of them in Jaramana.
Activists say more than 40,000 people have been killed since the uprising against President Bashar al-Assad began in March 2011.