Security sources said the attackers launched a three-pronged assault from the north, west and east of the city, encountering fierce fighting from Sunni Muslim militants on the second day of the battle to purge the city of terrorists.
In overnight fighting, U.S.-backed Iraqi forces captured the railway station in addition to the central hospital and parts of the city's western neighborhoods.
Witnesses said fierce battles with rockets, tank shells and automatic fire continued, and that militants claimed to have inflicted heavy casualties on U.S. and Iraqi forces.
The U.S. Army issued no statement on casualties.
Local sources said the bodies of dead gunmen littered the streets in the center of the city where the militants were barricaded.
They said U.S. warplanes had been targeting suspected hideouts of militants believed to include foreign fighters led by Abu Musaab al-Zarqawi, the suspected leader of al-Qaida in Iraq.
Earlier reports from northwest Fallujah said U.S. troops had encountered booby-trapped barricades, which they destroyed with tank fire, igniting massive explosions.
The Iraqi government has imposed a 24-hour curfew in the city.
Copyright 2004 by United Press International