The situation is tense since the US forces launched Operation River Blitz on Tuesday, Aljazeera has learned.
In the province's city of Ramadi, two Iraqis including a woman along with her children were killed in US fire.
While three civilians were injured when US troops opened fire on their car, the woman and children were killed when the air force bombed a house in Bu-Farraj district, north of the city.
Several checkpoints have been set up by the US forces in the city, with students studying at al-Anbar University unable to reach their classrooms, Aljazeera has learned.
The US action has enraged the citizens, particularly since troops killed at least five civilians and injured 16 in firing.
The US claims it is attempting to
US forces also launched arrest operations and shut-off many areas in the city, claiming they were attempting to capture al-Qaida leader Abu Musab al-Zarqawi.
The forces surrounded Hiyt city, imposing curfew for the seventh consecutive night. Aljazeera learned that the US forces had arrested many people including the medical staff of the Hiyt general hospital.
In Haditha, heavy US patrolling continued and a curfew has remained in place for four successive nights.
Citizens were being prevented from moving in and out of the city. The gates to the city had been shut by the US forces after they withdrew from the neighbouring al-Haqlaniya city.
A similar situation prevailed in al-Qaim from where several hundred families have fled towards al-Ana city fearing clashes between anti-US fighters and the troops.
In al-Rutba, US forces were barricading people from moving inside the city before 9am, and from exiting or entering it after 5pm.
The US troops had not revealed any timeframe of their military operation in al-Anbar province, Aljazeera has learned.