"A young man and a woman were killed in air strikes on Douma," the largest town in the Eastern Ghouta region, said Rami Abdel Rahman, head of the Syrian Observatory for Human Rights.
Raids also hit the town of Arbin, and regime artillery hit Harasta, leaving nearly two dozen people wounded in Eastern Ghouta.
"These are the first air strikes since the truce was announced" on Tuesday afternoon, Abdel Rahman said.
"The situation is tragic -- the heavy shelling is ongoing," said Zeina, a resident of Douma who spoke to AFP via the internet.
Russia's defence ministry on Tuesday declared a two-week "regime of silence" in Eastern Ghouta, the last opposition stronghold near the Syrian capital.
Hamza Bayraqdar, a spokesman for the Army of Islam, told AFP on Tuesday that the faction had not been notified about the ceasefire, but would not "reject any agreement to stop the bloodshed and suffering of our people".
"Russia's announcement of a cessation of hostilities in Eastern Ghouta is a political announcement -- militarily, it's not being executed," he told AFP.
"Russia wants to present itself as neutral and a sponsor of a political solution (to the Syrian conflict), but on the ground it's a different case," he said.
"This announcement came late. It was supposed to be announced on March 5, but the regime didn't commit to it. Even with this announcement, there is no agreement from the regime on a freeze."
It is the last remaining opposition stronghold near Damascus, where a string of local "reconciliation deals" have seen villages and towns brought back under the control of President Bashar al-Assad's government.
Russia and rebel backer Turkey sponsored a nationwide truce between Assad's forces and opposition fighters in December, but fighting has continued across swathes of Syria.
More than 310,000 have been killed since Syria's conflict began in March 2011.
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