A US defence official on Tuesday said initial reports indicated that scores of Iraqis attacked the marine position near the governor's palace in the city.
"There may have been as many as a dozen marine deaths," the official said, adding that a significant number of Iraqis were also killed in the exchange of fire.
The official said it was not clear exactly who had mounted the attack on the marines.
Ramadi, 80km west of the capital Baghdad, is close to Falluja – currently under siege by US occupation forces.
US soldiers are seeking to flush out Iraqi resistance fighters from the town and arrest those who killed four American contractors last week.
But reports coming from Falluja say the occupation forces are facing stiff resistance.
CNN said it appeared the attack in Ramadi had been carried out by supporters of the ousted Iraqi President Saddam Hussein and not by followers of the Shia leader Muqtada al-Sadr, whose fighters have been battling occupation troops in several places.