Operation Fallujah: 'Hizballah fighters' killed
Just hours after the battle's opening salvos, heavy fighting ensued between Iraqi forces and militants, with Baghdad's troops storming several towns.
Reports suggested the Shahabi, Harariyat and Dowayah towns on the outskirts of Fallujah were liberated by government forces involved in the battle, according to social media users.
Dozens of IS militants were also reportedly killed in the military operation to retake the city of Fallujah, announced Prime Minister Haider al-Abadi on Sunday night.
"We are beginning the operation to liberate Fallujah," he said in a statement. "The Iraqi flag will be raised high over the land of Fallujah."
Special Forces, regular soldiers, police, militia forces and pro-government tribesmen are taking part in the offensive to retake the city, located in Anbar province.
Iraq's military warned civilians still in Fallujah - estimated to number in the tens of thousands - to leave the city ahead of the operation, but residents said checkpoints controlled by IS fighters block all roads leading out of the city.
The US-led coalition, which is providing aerial military support for the government forces, recommended civilians who cannot leave raise a white flag above their homes.
Last week, the anti-IS coalition carried out seven airstrikes in the Fallujah area, while Iraq said it also bombed the city with US-supplied F-16 warplanes.
Fallujah is an IS stronghold just 50 km (30 miles) west of Baghdad, and has been out of government control since January 2014.
The city is "a safe haven for [the Islamic State group], where they can construct their bombs and plan their operations in relatively close proximity to Baghdad", said Steve Warren, the Baghdad-based spokesman for the US-led coalition in Iraq.
Fallujah and Mosul, the capital of the northern province of Nineveh, are the last two major cities IS holds in Iraq.
Abadi's announcement comes at a time when Iraqi ground forces backed by US-led coalition air support are gaining territory against IS, most recently in Iraq's vast western Anbar province.
Last week. Iraqi forces pushed IS out of the western town of Rutba, 380km (240 miles) west of Baghdad, on the edge of Anbar province. Last month, Iraqi forces cleared territory along Anbar's Euphrates river valley after the provincial capital, Ramadi, was declared fully liberated earlier this year.