Villager Mahmud Muhammad, an Iraqi civilian who helped rescue four people wounded in the incident, said on Friday the mother of the two girls and the driver of the car, who were both wounded, had told him a US tank had fired at the vehicle in Naamiya, 10km southeast of Falluja.
Two other children in the car were hurt.
Hospital officials in Falluja confirmed the casualties, but there has been no independent verification of the incident.
There was no immediate comment from the US military, which has intensified air and artillery strikes around Falluja in the past week in what it says is a drive against foreign fighters led by Jordanian fugitive Abu Musab al-Zarqawi.
It says al-Zarqawi, a declared al-Qaida ally, has bases in Falluja, but residents deny knowledge of al-Zarqawi's network and say US assaults kill civilians.
In other violence, a car bomb exploded near a police station
in Ishaqi, about 80km north of Baghdad, wounding two policemen, police said. Two prisoners escaped after the blast.
Police said the bomb was aimed at a passing US convoy. The US military had no immediate information on the attack.
US forces clashed with armed fighters near the town of Baquba, 65km north of the Iraqi capital. Four civilians were
wounded in the fighting in Buhroz village just south of Baquba.