Syrian capital and demanded the regime allow in aid convoys.
State media blamed the early-morning blast at the entrance to the mixed Christian-Druze suburb of Jaramana on "terrorists," the regime term for rebels, and said 16 civilians were wounded.
The Syrian Observatory for Human Rights said a suicide bomber from the al Qaeda-linked Al-Nusra Front detonated an explosives-packed car at the checkpoint between Jaramana and rebel-held Mleha.
Heavy fighting followed, with rebel mortar fire hitting Jaramana, said the Britain-based Observatory, which relies on activists and medics on the ground.
It said 16 soldiers and 15 jihadists were killed in the Jaramana clashes.
Observatory chief Rami Abdel Rahman said the southeastern suburb is a key pro-regime area and would be exposed if the rebels overran the checkpoint.
Several hours after the early morning bombing, rebels were still fighting troops for control of the checkpoint but government aircraft launched four strikes to try to repel them, he said.
One resident said the fighting was of an "unprecedented" level since Syria's conflict erupted in March 2011 and that mortar rounds crashed into Jaramana both in the morning and afternoon.
"It is very violent; we can hear automatic weapons fire, mortar rounds, bombardments," he told AFP by telephone.
The conflict, which erupted after President Bashar al-Assad launched a bloody crackdown on Arab Spring-inspired democracy protests, is believed to have killed more than 115,000 people.
Millions more have been forced to flee the country and hundreds of thousands are trapped by the fighting.
Washington condemned the regime's relentless siege of rebel-held Eastern Ghouta and Moadamiyet al-Sham on the capital's outskirts, and said it must allow relief convoys into these areas.
There were "unprecedented reports of children dying of malnutrition-related causes in areas that are only a few miles from Bashar al-Assad's palace in Damascus," said State Department spokeswoman Jen Psaki.
"The regime's deliberate prevention of the delivery of lifesaving humanitarian supplies to thousands of civilians is unconscionable," she said.
Envoy begins peace push
UN-Arab League envoy Lakhdar Brahimi arrived in Cairo on Saturday to launch a regional tour aimed at paving the way for a peace conference in Geneva next month.
But prospects for the meeting remain unclear, with Syria's opposition divided and due to vote next week on whether to take part and the Assad government saying he will bow to rebels and quit.
In Geneva, spokeswoman Khawla Mattar said Brahimi would meet Egypt's foreign minister as well as the head of the Arab League and then head for talks in Syria and in Damascus ally Iran.
The push for the Geneva talks will also be high on the agenda of US Secretary of State John Kerry who heads to Europe to attend a "Friends of Syria" group meeting in Britain on Tuesday.
World powers have for months been pressing for a negotiated solution to the Syrian conflict, and the renewed push comes after Syria accepted in September a US-Russia deal to hand over its chemical arsenal for destruction.
But the political opposition remains divided amid tensions on the battlefront between mainstream fighters and jihadists.
The main National Coalition opposition bloc said members will decide next week whether to attend the Geneva talks, while coalition member Syrian National Council has threatened to quit if they do.
Meanwhile, al Qaeda loyalists of the Islamic State of Iraq and the Levant (ISIS) have captured at least 35 mainstream rebels of the Free Syrian Army in the northern city of Aleppo, the Observatory said.
Tensions between FSA loyalists and the ISIS have spiralled in recent months, especially in northern Syria where the opposition controls vast swathes of territory.
Elsewhere, Lebanon said that nine Lebanese Shiites reportedly freed by Syrian rebels have been transferred to Turkey but will only go home if some 200 prisoners are released from Syrian jails.
Turkey has said it hopes the operation will lead to the release of two Turkish Airlines pilots whose abduction in Lebanon was linked to the capture of the Lebanese.