American forces entered Falluja for the first time since the war with Iraq started on Sunday.
One Iraqi witness said the troops took over a school when they arrived, and the demonstrators just wanted them to leave the school so they could use it.
But US forces insisted they had been fired on by the protesters.
In other Iraq news:
One of Saddam Hussein's top advisers, Amer Mohammed Rasheed, is said to have handed himself in to US forces.
He is said to have been involved in making secret weapons before he became Iraq's oil minister in 1995.