Fighting has erupted in a Damascus suburb and around an army base in northern Syria, according to opposition sources.
It came hours after the start of a truce marking a Muslim holiday of Eid al-Adha.
Activists say three people were killed by tank fire and snipers in Harasta, a town near Damascus.
Syria’s president Bashar al-Assad began the day with prayers at a Damascus mosque live on state television, just after his armed forces announced a conditional ceasefire in the conflict that has killed 32,000 people.
But the army has warned that it will respond to any rebel attacks, or moves to exploit the truce to reinforce or resupply insurgents who have seized control of several parts of the country.
A commander from the rebel Free Syrian Army said his fighters would also honour the ceasefire but demanded Assad meet rebel demands for the release of thousands of detainees.
The Syrian Observatory for Human Rights said rebels were trying to storm the Wadi al-Daif army base, which is less than 1 km 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.
Calm across Syria in early hours of ceasefire