The Friday attacks added to the deteriorating humanitarian situation in the city as hospitals in the area continued to suffer major shortages in medical supplies.
US air strikes on Falluja have killed scores of civilians in recent weeks.
US marines have been fighting Iraqis opposed to a foreign military presence in Falluja for months, but the intensity of fighting has increased dramatically in the last four days.
The US military says it is targeting supporters of Abu Musab al-Zarqawi, a Jordanian whom the US accuses of being an al-Qaida operative.
Al-Sadr supporters shot
Elsewhere in Iraq violence continued. Iraqi troops opened fire on hundreds of supporters of Muqtada al-Sadr as they left a Baghdad mosque after Friday prayers, killing two men and wounding five people, doctors and witnesses said.
The marchers were chanting slogans supporting al-Sadr when they were fired at by Iraqi National Guards near the Kadhimya neighbourhood in northern Baghdad, witnesses said.
Iraqi troops killed two and injured
five al-Sadr supporters
A doctor at Naaman hospital said two men were killed in the violence. It was not immediately clear what prompted the Iraqi troops to fire.
A source at al-Sadr's office said the marchers were unarmed.
An Iraqi group has threatened to kill four Iraqi policemen seized in Najaf unless police agree to stop hunting insurgents and pressuring al-Sadr, Aljazeera reported.
The group threatened to kill the hostages within 72 hours unless their demands were met
Meanwhile, three Lebanese, one of them a woman, were shot dead in Baghdad on Friday morning in a botched abduction attempt, the Lebanese Foreign Ministry announced in Beirut.
Businessmen Gibran Badine and Karim Khury along with Khury's wife, were shot dead at one of their homes, the ministry said.
The two men ran a food import business with an Iraqi associate.