Kurdish forces are also attempting to take back the city of Mosul, while ISIS militants have stepped up suicide bombings across Iraq.
The city has been under ISIS control for over two years. The bid to take back the city is being supported by paramilitary troops, and is receiving aerial assistance from the U.S.-led coalition, the Associated Press reported.
Fallujah is considered important to ISIS because it acts as a staging ground from which they undertake attacks in Baghdad and Sadr City.
Earlier this month, Baghdad and Sadr City were hit by three bombs in the space of just a few hours, killing 80 people on the deadliest the Iraqi capital had seen in a year.
If the recapturing of Fallujah is successful, ISIS will be pinned back towards the city of Mosul, which effectively acts as the capital of the territory the group has captured in Iraq. This means militants would have greater difficulty in making further advances in the country.