Three people were killed by tank fire and snipers in Harasta, a town near Damascus, activists said.
The Syrian military had said it would hold fire on Friday morning following an appeal by international mediator Lakhdar Brahimi for a pause in fighting which has killed 32 000 people and which threatens to draw regional powers into the conflict.
But violations by both sides swiftly marred the truce.
Rebels in a northern town near the Turkish border said a sniper had killed one of their fighters early on Friday and a Reuters journalist there heard the sound of four tank rounds.
"We don't believe the ceasefire will work," rebel commander Basel Eissa told Reuters. "There's no Eid for us rebels on the front line. The only Eid we can celebrate will be liberation."
The Syrian Observatory for Human Rights said rebels were trying to storm the Wadi al-Daif army base, which is less than 1km from the Damascus-Aleppo highway and that troops had fired artillery at a nearby village.
Citing opposition activists, the British-based group also said the army had fired six rockets at the besieged Khalidiya district of Homs, wounding two people and damaging houses.
President Bashar al-Assad's forces had announced conditional acceptance of a cease fire on Thursday night.
"On the occasion of the blessed Eid al-Adha, the general command of the army and armed forces announces a halt to military operations on the territory of the Syrian Arab Republic, from Friday morning … until Monday," the army said.
Exploiting the truce
But it warned it would respond to any rebel attacks, or moves to exploit the truce to reinforce or resupply insurgents.
A commander from the rebel Free Syrian Army had said his fighters would also honour the ceasefire but demanded Assad meet opposition demands for the release of thousands of detainees.
Some Islamist fighters, including the Nusra Front, dismissed the truce before it even came into effect, but after a night of clashes in Aleppo, Damascus and the west of the country, activists had reported an initial lull in hostilities.
One exception was the southern town of Inkhil, where three people were wounded as they tried to protest after special prayers in a mosque to mark the start of the Eid, according to Rami Abdulrahman, head of the Syrian Observatory.
Several other demonstrations in the southern province of Dera'a, cradle of the protests which erupted against Assad in March last year, were also broken up, Abdulrahman said.
Assad himself, who has vowed to defeat what he says are Islamist fighters backed by Syria's enemies abroad, was shown on state television attending Eid prayers at a Damascus mosque.
Damascus residents said on Thursday night troops stationed on a mountain overlooking Damascus targeted Hajar al-Aswad, a poor district inhabited by refugees from the Israeli-occupied Golan Heights. There were no immediate reports of casualties.
"Consecutive artillery volleys from Qasioun shook my home," said an engineer who lives in al-Muhajereen district on a foothill of the mountain, giving his name only as Omar.
'We do not care about this truce'
The fighting pits mainly Sunni Muslim rebels against Assad, from the minority Alawite sect which is distantly related to Shi'ite Islam. Brahimi has warned that the conflict could suck in Sunni and Shi'ite powers across the Middle East.
Qassem Saadeddine, head of the military council in Homs province and spokesman for the FSA joint command, said on Thursday his fighters were committed to the truce, but demanded the release of detainees by Friday morning.
Abu Moaz, spokesperson for Ansar al-Islam, which includes several brigades fighting in and around Damascus, said the Islamist group doubted Assad's forces would observe the truce, though it might suspend operations if they did.
"We do not care about this truce. We are cautious. If the tanks are still there and the checkpoints are still there then what is the truce?" he asked.
Brahimi's predecessor, former UN chief Kofi Annan, declared a ceasefire in Syria on April 12, but it soon became a dead letter, along with the rest of his six-point peace plan.
Violence has intensified since then, with daily death tolls compiled by opposition monitoring groups often exceeding 200.
UN aid agencies have geared up to take advantage of any window of opportunity provided by a ceasefire to go to areas hard to access due to fighting, a UN official in Geneva said.
The UN refugee agency UNHCR said it had prepared emergency kits for distribution for up to 13 000 families – an estimated 65 000 people – in Homs and the northeastern city of Hassaka. – Reuters