Iraqi forces have clashed with ISIS militants after an offensive against the town of Falluja was announced by Iraq's Prime Minister.

Residents were told to leave the militants' stronghold on Sunday but many were prevented by roadside bombs left by ISIS fighters. The city, surrounded by Iraqi forces since last year, was subjected to a night of heavy bombardment, after Prime Minister Haider al-Abadi used his official twitter account to announce the campaign.

"Zero hour for the liberation of Falluja has arrived. The moment of great victory has drawn near and Daesh has no choice but to flee," Abadi tweeted.

He said the offensive would be conducted by the army, police, counterterrorism forces, local tribal fighters and a coalition of mostly Shi'ite Muslim militias. A US-led coalition that has bombed Islamic State in Iraq and neighboring Syria for nearly two years is expected to provide air support.

Falluja, a longtime bastion of Sunni Muslim jihadists, 50 km (30 miles) west of Baghdad, was the first city to fall to the jihadists in January 2014, six months before the group declared a caliphate spanning large parts of Iraq and Syria.

Known as the "City of Minarets and Mother of Mosques", Falluja is seen as a focus for Sunni Muslim faith and identity in Iraq.

Officials said Shi'ite militias, including ones backed by neighbouring Iran, may be restricted to operating outside the city proper, as they were largely in the battle for Ramadi, to avoid aggravating sectarian tensions with Sunni residents.

The Iraqi army, police and the militias, backed by coalition air strikes, have surrounded Falluja since late last year, while the jihadists have been preventing residents from leaving for months. However an offensive has been delayed while the coalition focused on re-capturing ISIS held territory in the north and west of Iraq.

The military's media unit told families who cannot flee to raise white flags to mark their location in the city.

Deputy District Council Chairman Falih al-Essawi said three corridors would be opened for civilians to camps west, southwest and southeast of the city, and a subsequent military statement said some residents had begun to flee.

"Our goal is to liberate civilians from Daesh's repression and terrorism," Abadi said in a televised speech.

Aid has not reached the city since December 2015 when the Iraqi military recaptured the nearby city of Ramadi. Both the United Nations and Human Rights Watch warned that residents in Fallujah faced severe food and medical shortages during the government's siege.

Residents told Reuters about 20 families set out from a southern front-line neighbourhood late on Saturday but that only half of them made it out. Some were intercepted by Islamic State, while others were killed by explosives planted along the road by the jihadists.

Saad al-Hadithi, a spokesman for Abadi, said the city's "liberation" would help restore normal life to Anbar province, over which Islamic State took nearly complete control in 2014.

Following recent government offensives in Rutba and Hit, control of Falluja would secure the road more than 500 km (300 miles) from Baghdad to the Jordanian border and northwards to Haditha, 190 km (115 miles) northwest of the capital.

But Islamic State still controls vast swathes of territory and major cities such as Mosul in the north. Iraqi authorities have pledged to retake Mosul this year, although some officials question in private whether the army will be ready in time.

Additional reporting by Reuters.