The violence came as thousands of people across Syria defied the government crackdown to remember a notorious 1982 massacre in the central city of Hama that killed thousands.
The commemorations took place as Western and Arab countries sought to reach agreement on a draft UN resolution to pressure Syria to end its nearly 11-month crackdown on anti-regime dissent.
A new text being considered by the UN Security Council does not explicitly call on President Bashar al-Assad to step down or mention an arms embargo or sanctions, but "fully supports" an Arab League plan to facilitate a democratic transition.
Diplomats said the new draft took into account concerns by Moscow, a staunch Damascus ally.
But Russia poured cold water on such hopes on Friday, saying it could not support the latest draft in its current form.
"Some of our concerns and the concerns of those who think the same as us have been taken into consideration but all the same this is not enough for us to be able to support it in this form," Deputy Foreign Minister Gennady Gatilov said.
"We still have a whole number of concerns over the content of this text and we will be ready to continue consultations on the draft resolution," he said.
"We are ready to continue work on modifying it, taking into consideration and based on our principled positions," he said, adding that no vote was expected on Saturday or Sunday.
However, officials said US Secretary of State Hillary Clinton held "constructive" talks with her Russian counterpart, Sergei Lavrov, over the draft.
The two agreed that teams from both countries would "continue to consult" on the draft in New York, State Department spokesman Mark Toner said.
At least 25 people were reported killed across Syria on Friday, among them 14 civilians, the Syrian Observatory for Human Rights said.
The Britain-based group said 11 soldiers were killed in clashes with the rebel Free Syrian Army (FSA) in the southern province of Daraa and in Homs.
In addition, one person died of wounds sustained on Thursday, and the bodies of three other people were found or returned to their families.
Amid growing concern that Syria is sliding into all-out civil war, an officer with the FSA claimed the regular army "is in a pitiful state and getting close to collapsing."
Major Maher Nouaimi, based in Turkey, told AFP by telephone that "even though the army has huge military capabilities, soldiers no longer have the will to fight or are ready to do so."
He said there was growing discontent among officers and the rank and file against commanders, who are largely drawn from Assad's Alawite community, an offshoot of Shiite Islam.
Most conscripts in the military are from Syria's majority Sunni Muslim community.
In many instances, Nouaimi said, dissident soldiers have literally had to fight their way out, braving security forces checkpoints to escape.
Osama Shami, a spokesman for activists in the Damascus region, said several rallies took place in the capital, with security forces opening fire on demonstrators.
"Government troops deployed heavily around mosques but protesters managed to evade them by leaving Friday prayers quietly and then holding spontaneous protests in alleyways," he told AFP.
"Hafez is dead, Hama is not! Bashar will die and Syria will not!" read placards brandished by protesters in the Al-Kidam district of Damascus, according to an Internet video posted by militants.
Hafez al-Assad was the father and predecessor of the current president. According to various estimates, between 10,000 and 40,000 people died during the 27-day 1982 onslaught he ordered against an Islamist uprising in Hama.
The current violence has killed at least 6,000 people since it erupted last March, rights groups estimate.
Human Rights Watch said in a report released on Friday that children as young as 13 are a particular target in the "rampant" use of torture by government forces battling opposition protests.
While the United Nations says hundreds of children have been killed in the crackdown, HRW highlighted cases of children shot in their homes or on the street, or grabbed from schools and then tortured.
"Children, some as young as 13, reported to Human Rights Watch that officers kept them in solitary confinement, severely beat and electrocuted them, burned them with cigarettes, and left them to dangle from metal handcuffs for hours at a time, centimetres above the floor," said the report.