Sunday marked the heaviest day of attacks, witnesses said, as warplanes bombed a market area, the al-Dahi mosque, a building used as a warehouse and two other locations, killing at least 14 people and wounding 26 others.
At least 31 people were killed and more than 82 wounded in the three days of ground and air assaults on Falluja, according to the two witnesses and a medical source in the city.
The dead and wounded included women and children, the sources said.
ISIS posted videos of what it said were warplanes flying over Falluja, along with footage of the damaged markets and still images of the damaged mosque and several hospitalized victims of the attacks. ISIS claims women and children are among the dead and wounded.
The Iraqi army, backed by paramilitary forces and the country's air force, carried out operations in Karma, northeast of Falluja, and other nearby villages, two Iraqi military officials told CNN.
The operations destroyed eight suicide car bombs belonging to ISIS, the officials said, adding that the Iraqi Security Forces will continue fighting in the area until they defeat ISIS.
The Iraqi Ministry of Defense released a video showing military movements in Salaheddin province's Syed Ghraib, which the military says is newly liberated. The town is located just northwest of Dujail, about 70 kilometers (45 miles) north of Baghdad.
The video shows military engineers defusing bombs planted by ISIS, and at one point, a military officer climbs a ramp to a post where an ISIS flag flies. He throws it to the ground and replaces it with an Iraqi flag.
Operations in the western side of Salaheddin province and the northeastern portion of Anbar province are intended to cut off ISIS supply routes from Baiji into the strongholds of Falluja and Ramadi.
Falluja and its surrounding villages are under ISIS control. At least 100,000 civilians are trapped inside, two sources inside Falluja said. Only the elderly and those with medical issues are allowed to leave, the sources said.
Since ISIS seized the city in January 2014, a total of 2,839 people have been killed, including 211 women and 360 children, the medical source in Falluja said. Fighting has also wounded another 4,704 people, the source said.
Last week, the Iraqi military launched a major operation to liberate Anbar province, where Falluja is located, and the adjacent Salaheddin province, which lie to the west and northwest of Baghdad, respectively.
The Iraqi military announced the operation about a week after the militant group overran Anbar's provincial capital, Ramadi
Iraqi soldiers and security forces are fighting alongside a key Shia militia group, Hashd al-Shaabi, as they seek to push back the Sunni extremist militants.