State media said the "terrorist" bomber struck near a church of an order of the Maronite church, killing four people and wounding four others.
"Terrorists" is the term the government in Damascus uses for rebels in Syria.
Confirming the toll, the Britain-based Syrian Observatory for Human Rights said "a suicide bomber detonated his explosives near the Mariamite church."
It also reported shelling in nearby al-Amin Street, also in old Damascus, but gave no more details.
In a statement issued later, it said the bodies of 16 men who died under torture at the hands of Syria's security forces had been handed to their families.
It said the men had been from Harasta, one of a number of rebel strongholds near Damascus that have come under immense army pressure in recent weeks, as the regime has pressed a campaign to secure the capital.
"It happens all too frequently that the bodies of detainees with torture marks are handed back to their families," Observatory director Rami Abdel Rahman told AFP.
"I fear for the lives of thousands of other detainees."
Elsewhere, regime forces stormed the town of al-Qariatayn in the central province of Homs, state television said, and "restored peace and security".
The Observatory said troops in the town were detaining people.
North of Homs city, the army intensified its bombardment of rebel-held Rastan and Talbisseh.
The army also renewed its shelling of the town of Houla, scene of a massacre last year, according to the Local Coordination Committees, a network of activists.
The Observatory reported the army has retaken parts of the Barzeh district in Damascus from rebels.
The latest violence in a conflict the Observatory says has killed more than 100,000 people comes as relief groups say they are unable to keep pace with the rising misery.
"There is a huge discrepancy between the ability to cope with the Syrian crisis and the escalating speed in which the demands in Syria are growing," said Peter Maurer, the head of the International Committee of the Red Cross (ICRC).
"And this gap still continues to widen as we speak," he said in Geneva, decrying "incredible violence and incredible suffering, and quite extraordinary violations of international humanitarian law by all parties to the conflict in Syria."
On Tuesday, the World Food Programme warned that Syrians caught up in the war were cutting basic foods from their diets to save money, or begging to survive.
Maurer, presenting the ICRC's 2012 annual report, said the Syrian conflict represented the organisation's largest outlay, with $107.2 million dedicated to addressing it this year.
Turkish Foreign Minister Ahmet Davutoglu met the top UN expert leading a probe into allegations of chemical weapons use in Syria, a ministry official in Ankara said.
Davutoglu held closed-door talks with Swedish expert Ake Sellstrom, who has so far been barred from entering Syria.
As US Secretary of State John Kerry discussed Syria with Jordan's King Abdullah II in Amman, Russia accused Saudi Arabia and other Gulf states of funding "terror".
It was responding to accusations by Saudi Foreign Minister Prince Saud al-Faisal that Russia was responsible for mass killings in Syria because of its military support for the regime.
"A number of capitals, including Riyadh, unfortunately are not ashamed of employing all sorts of methods and contacts, including by financing and arming international terrorists and extremists," a Russian foreign ministry statement said.
Refugees from Syria have flooded across borders into neighboring states in an effort to flee the conflict which has also spill militarily into other countries.
More than 1.6 million Syrians, including more than 800,000 children, have sought refuge in Lebanon, Jordan and Turkey.
On Thursday, the UN Security Council backed UN peacekeepers in the Golan Heights carrying machine guns, as fallout from the Syria war increased in the ceasefire zone.
The 15-member council passed a resolution to extend the mandate of the force, which monitors a three-decade-old ceasefire between Syria and Israel. The resolution called on Syrian government and opposition fighters to stay out of the zone.
UN officials and diplomats said the peacekeepers, which traditionally only carry very light arms, will get machine guns, extra body armor and more armored vehicles.
The Golan has been tense since the beginning of the conflict in Syria more than two years ago.
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Actually, that was a shell, not a suicide bomber. FSA attack Shabiha and Assad's thugs, they have no business killin Christians.
There is a video of shell falling in the area, its just that you people do not speak arabic and sources such as Presstv and Irani child murdering pigs said it and you follow it without even confirming
Shameless west and immoral Muslim nations are destroying the homes of helpless innocent Syrians. I feel almost like crying for the common Syrians. What a man made human tragedy. West is playing dirty great game with the lives of innocent Syrians and Muslims are playing in their hands. What a way of taking revenge.