Ramadi is the regional capital of Al-Anbar province, a stronghold of Sunni insurgents and a prime base for Al-Qaeda operators.
Meanwhile in the central city of Al-Diwaniyah, at least one man was reported killed and several wounded in clashes between joint Iraqi and U.S. forces and unidentified gunmen.
The attacks came a day after at least five U.S. soldiers were killed by roadside bombs.
The U.S. military said a roadside bomb blast killed one more U.S. soldier and wounded two others in Diyala province, north of Baghdad on April 5. Earlier, the military said four U.S. soldiers were killed by roadside bombs in Baghdad.
Also on April 5, four British soldiers and a civilian interpreter were killed in a roadside bombing near the southern city of Al-Basrah. Ten Iraqi soldiers were killed in an attack near the northern city of Mosul.
(compiled from agency reports)