The U.S. military says Iraqi army troops backed by U.S. forces moved into the city early Friday morning to disrupt activities of a Shi'ite militia loyal to anti-American cleric Moqtada al-Sadr.
City residents reported of fighting between militia gunmen and coalition troops. They said soldiers also were conducting house-to-house searches and making arrests, after imposing a strict curfew.
There were no immediate report of casualties.
Separately, a suicide car bomber struck a police checkpoint in western Ramadi Friday, killing at least 20 people and wounding 30 others.
A top local police official said two policemen were among the dead.
Ramadi is the capital of the restive Al Anbar province, which has been a stronghold of Sunni insurgency. But recently many tribes have switched sides and joined the Iraqi police and army in an attempt to expel al-Qaida in Iraq fighters from their region.
Some information for this report was provided by AP and Reuters.