The Syrian Observatory for Human Rights and local residents also reported violations in a second "de-escalation zone" in the central province of Homs.
The areas - in addition to a third ceasefire zone in the south - were announced in recent weeks by Syrian government ally Russia.
But today, government bombardment on the zone near Damascus killed three civilians and wounded seven more.
"The shelling hit the town of Hammuriyeh early today, killing a woman, a man, and a child," said Observatory head Rami Abdel Rahman.
Air strikes have also pummelled rebel-held parts of the Jobar district of Damascus and the adjacent district of Ain Tarma.
Further south, one man was killed in Syrian government air strikes in the northern parts of Homs province, according to the Observatory and a resident.
The raids were the first since the ceasefire in Homs was announced one week ago.
"Four air strikes hit Al-Houla today," resident Abbas Abu Osama told AFP, adding that four other surrounding towns were hit with one air strike each.
Abdel Rahman confirmed that a man was killed in a raid but could not specify whether he was a rebel fighter or civilian.
Under a plan hammered out in May between Russia, Turkey and Iran at peace talks in Kazakhstan, four "de-escalation zones" were to be established across swathes of Syria.
Last month, Moscow announced the establishment of the first two zones in southern Syria and in the rebel stronghold of Eastern Ghouta near Damascus.
The zone in Homs province was announced on August 3.
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