According to independent Iraqi journalist Fadhil al-Badrani, US warplanes targeted Falluja's eastern and southern districts.
He said fierce clashes had broken out in the city centre between US forces who have been in the city since 8 November and Iraqi fighters who had infiltrated back in across the Euphrates river.
"There is no way to determine the number of casualties as US authorities have barred journalists and aid workers from entering Falluja," al-Badrani told Aljazeera.
Falluja return delayed
The US military had earlier said it could not recommend to the Iraqi interim government the return of residents to Falluja.
US soldiers have been engaged
in fierce fighting in Falluja
"At some point we will make a recommendation; we have not reached that point," Lieutenant Colonel Dan Wilson, a deputy commander of the First Marine Expeditionary Force, told reporters in a military base near Falluja late on Friday.
The Iraqi interim government had promised on Thursday residents could begin returning to the city, west of Baghdad, as early as next week, saying that basic services and aid had been restored.
But US marines, backed by a small Iraqi force, are apparently still engaged in fighting with the city's remaining resistance. There are also fears that some civilians may be trapped.
"We know of 150 civilians trapped in the city," al-Badrani said.
Elections staff targeted
Meanwhile in the capital, witnesses said an armed group fired on a police car as it drove through central Baghdad on Sunday, then dragged three passengers from the vehicle and shot them dead. The vehicle was then set on fire.
Attacks on election officials have
surged throughout Iraq
Witnesses said the people pulled from the car were wearing civilian clothes although they were travelling in a police car.
A spokesman for the Electoral Commission, Farid Ayar, said the three were staff members from an Iraqi elections office.
The attack occurred in Haifa Street, a major thoroughfare in downtown Baghdad that has become a focal point of attacks.
Fighters armed with AK-47 assault rifles and pistols then set up a roadblock on the street, stopping and searching every car that passed, pointing their guns in through the windows, the witnesses said. Some scenes were filmed by Reuters Television.
There were no police or US forces in the area. The police source said units were unable to get to the scene.
The attack on elections workers is the second in as many days. On Saturday, two people were killed and eight wounded in a mortar attack on an election office north of Baghdad, police and hospital sources said.
They said five mortars landed on the premises in Dujail, one of many around the country providing information to potential voters before the 30 January election. It will be used as a polling station on the day of the vote in six weeks' time.
Among the wounded were six Iraqi security personnel, who were guarding the office against attack in the predominantly Sunni town, about 50km north of the capital.