Government forces comprised of both soldiers and police are attempting to retake the city from the Islamic State of Iraq and Syria, which seized control in December.
As of Friday, many fighters were reported killed in the operation, and large number of weapons have been confiscated. Health officials said that Friday's shelling killed at least 13 people and wounded 27 others.
More than 300 people, mostly civilians, have died since the beginning of the year.
Fallujah is home to an estimated 700,000 people and is situated in Anbar province, west of Baghdad.