"Fighting broke at around 12:30 pm (0830 GMT) as the insurgents opened fire at the US forces near the police station," resident Mohammed Sleiman told AFP.
"The Americans then called over loudspeaker for residents to stay away from the clashes and to hand over the terrorists," the witness said.
The marines denied knowledge of the clashes, but said that a mortar fired by insurgents had hit a house in Karma, causing civilian casualties.
Fallujah, a Sunni Muslim bastion, was rocked in April by the heaviest fighting in Iraq since the US-led invasion last year, but has been relatively calm since US troops handed over patrols to Iraqi police and the newly-formed Fallujah Brigade, an ad-hoc force of army veterans.
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