Earlier, U.S. tanks reportedly fired on insurgent positions on the eastern edge of the city.
Insurgents retaliated with small arms fire, mortar rounds and rocket-propelled grenades.
Iraq's interim government today renewed its call to residents of Al-Fallujah to hand over insurgents or face a large-scale offensive.
In other violence, Iraqi police today said that nine Iraqi policemen were ambushed and killed yesterday in Al-Latifiyah, south of Baghdad.
[For the latest news on Iraq, see RFE/RL's webpage on "The New Iraq".]