The strikes today included two on the outskirts of Douma, the main town in Eastern Ghouta, according to the Britain-based Syrian Observatory for Human Rights.
Regime air strikes and artillery have been pounding the enclave near Damascus since February 18, with at least 519 dead since the bombing campaign was launched, according to the Observatory.
The Security Council on Saturday unanimously demanded a 30-day ceasefire to allow for humanitarian aid deliveries and medical evacuations. The measure did not specify when the truce would go into force beyond saying it should be "without delay".
There were no immediate details on casualties.
Abdel Rahman said there were also clashes in the south of Eastern Ghouta between regime forces and fighters from the Jaish al-Islam rebel group. Fighting in the area is frequent so it was not immediately clear if the clashes represented a change on the ground.
An AFP correspondent in Douma was able to hear the air raids and artillery strikes.