The Britain-based Syrian Observatory for Human Rights said air strikes battered the town of Hammuriyeh in Eastern Ghouta, leaving nine civilians dead.
Another nine, including a woman, were killed in air raids, artillery fire, and rockets that hit elsewhere in the enclave.
"The regime is bombing Eastern Ghouta to pave the way for a ground offensive," said Observatory head Rami Abdel Rahman.
Held by rebels since 2012, Eastern Ghouta is now the last opposition-controlled pocket around Damascus.
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The Observatory and Syrian daily newspaper Al-Watan had said negotiations were under way for the evacuation of jihadists from the enclave.
But government forces ramped up military pressure on Eastern Ghouta starting Sunday, sending more than 260 rockets sailing onto opposition-controlled towns there.
The bombing continued Monday, sending terrified civilians in the enclave searching for cover, AFP's correspondents said.