In a statement carried on state television, Syria's armed forces said the freeze would begin at 1:00 am on Saturday (2200 GMT Friday).
It would last for 24 hours in Damascus and the nearby rebel bastion of Eastern Ghouta, and for 72 hours in the coastal province of Latakia, the heartland of President Bashar al-Assad's Alawite sect.
There was no mention of Aleppo, where a week of fighting has killed more than 200 civilians.
"The Americans asked for Aleppo to be included, but the Russians refused," the source said.
More From This Section
Russia is a key backer of Assad's regime, while the US has supported various opposition factions in the country.
A diplomatic source quoted by Russian state news agency RIA Novosti said that Moscow and Washington, co-chairs of the International Syria Support Group, "are the guarantors of the 'regime of silence' implementation by the sides."