"Regime forces backed by tanks stormed Douma under heavy gunfire," the revolutionary council of Damascus province, where Douma is located, said in a statement.
An activist video posted online showed columns of smoke billowing into the sky over Douma, a stronghold of anti-regime dissent 10 kilometres (six miles) north of Damascus. Heavy gunfire could be heard in the background.
The Syrian Observatory for Human Rights monitoring group said gunfire killed two civilians in Douma on Sunday morning, while a third civilian was shot dead overnight in another part of Damascus province.
"Regime forces enter Douma each day but today's assault was the largest," Damascus revolutionary council member Mohammed Saeed told AFP.
The reports could not be independently verified.
The violence comes a day after the United Nations Security Council voted unanimously to dispatch 300 unarmed observers to Syria to monitor a UN-Arab League ceasefire that went into effect April 12.
At the same time an advance team of UN observers were touring Syrian hot spots on Sunday, while two monitors set up base in the flashpoint central province of Homs to ensure the end of months of bloodshed.
With a population of 100,000 residents, Douma has been at the forefront of more than a year of anti-regime protests that have been crushed with deadly force with forces of President Bashar al-Assad's regime.
In January rebels briefly seized control of Douma but the army quickly regained control of the suburb.
Copyright AFP (Agence France-Presse), 2012