Aljazeera's correspondent in Baghdad said six US armoured vehicles tried to enter the city, 50km west of the capital, from the east around 10.30am on Saturday.
However, the tough response by its defenders drove them back, he said.
There was a short exchange of fire between Iraqi fighters, who used rocket-propelled grenades (RPGs) and machine guns, and US forces backed by warplanes and artillery. Several properties were destroyed in the fighting.
"Look at my house, it is destroyed. Now the US officials will announce that my house was a shelter for Abu Musab al-Zarqawi. Please go inside and search, if you find a pistol, I will accept anything they say," a distraught man told Aljazeera.
Muhammed Dulaimi, a doctor at the city's general hospital, said most of the dead and injured came from a single family whose house was hit.
Reuters Television pictures showed Falluja fighters using mortars and RPGs. They also showed two trucks, carrying temporary accommodation, ablaze on a highway next to the city.
Several factory buildings and workshops in an industrial area of the city were also damaged or set on fire.