Iraqi troops attacked ISIL's last bastion on Thursday as the retreating militants battled to retain territory.
The launch of the keenly awaited offensive that the US-led coalition fighting ISIL has dubbed "the last big fight" of the campaign came even as Iraqi troops launched a new operation against the Kurds.
There had been fears the bitter dispute that has raged between the central government in Baghdad and Iraqi Kurdish leaders since the latter held a referendum for independence last month would hamper the battle against the militants.
But federal troops and allied paramilitaries pressed ahead with a threatened drive up the Euphrates valley towards the Syrian border in a bid to retake two Sunni Arab towns — Al Qaim and Rawa — that have been bastions of insurgency since soon after the US-led invasion of 2003.
Iraqi forces have retaken more than 90 per cent of the territory ISIL seized in the country in 2014, with the extremists now confined to a small stretch of the valley adjoining some of the last areas they still hold in Syria.
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"The heroic legions are advancing into the last den of terrorism in Iraq to liberate Al Qaim, Rawa and the surrounding villages and hamlets," prime minister Haider Al Abadi said from neighbouring Iran where he is on a state visit.
"They will all return to the arms of the motherland thanks to the determination and endurance of our fighting heroes," he added.
"The people of IS have no choice but to die or surrender."
Regional operations commander General Qassem Al Mohammedi said government forces were advancing on four fronts — from the east, south-east, north and south.
He said units of the federal police and the elite Counter-Terrorism Service as well as the mainly Shiite paramilitary Hashed Al Shaabi (Popular Mobilisation Forces) were supporting the army.
Crucially for an offensive in an overwhelmingly Sunni Arab region, Sunni tribal volunteers in the Hashed were heavily engaged alongside the Iran-trained Shiite militias that are its mainstay.
Provincial operations commander General Mahmud Al Fellahi said both Iraqi and coalition warplanes were carrying out heavy strikes.
Al Qaim has been renowned as a bastion of Sunni Arab insurgency for years.
US troops carried out repeated operations with names like Matador and Steel Curtain in 2005 to flush out Al Qaeda militants.
Coalition commanders are convinced that Al Qaim will be ISIL's last stand in its ambitions to territorial control of the cross-border so-called "caliphate" it proclaimed in 2014.
On the Syrian side of the border, Russian-backed government forces have been pushing down the Euphrates valley while US-backed Kurdish and Arab fighters have been attacking the jihadists from their stronghold in the north.
The launch of the offensive against ISIL's last Iraqi redoubt comes with federal troops and militias engaged in an operation to reassert central government control over thousands of square kilometres of territory long disputed with the Kurds.
Loss of the territory has dealt a crippling blow to the finances of the autonomous Kurdish region and on Wednesday its leaders reached out for talks with Baghdad, saying they were ready to freeze the outcome of the September 25 independence referendum.
The Iraqi prime minister on Thursday dismissed the offer, saying it did not go far enough.
"We will accept nothing but the annulment of the referendum and respect for the constitution," he said in a statement released by his Baghdad office.
Mr Al Abadi, whose stock has been massively boosted by the success of the fightback against ISIL, was in Tehran for talks a day after holding meetings in Ankara.
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On Thursday, his forces launched a new assault on Kurdish forces in a disputed oil-rich area of Nineveh province near the Turkish border using heavy artillery, Kurdish authorities said.
"They are advancing towards peshmerga positions," the top defence body of the autonomous Kurdish regional government said.
Parts of Nineveh province north and east of Iraq's second city Mosul are some of the last areas still held by Kurdish forces outside of the long-standing autonomous Kurdish region.
Kurdish leaders have long argued that the historic Kurdish majorities of disputed areas means they should be incorporated in their autonomous region and had taken advantage of the chaos of the war against ISIL to wrest control of many of them.
Thursday's assault was reported to be close to the route of a strategic oil export pipeline linking the Kirkuk fields with the Turkish Mediterranean port of Ceyhan which fell into disuse during ISIL's lightning sweep through northern and western Iraq in 2014.
Mr Al Abadi discussed reopening the pipeline in his talks with Turkish president Recep Tayyip Erdogan on Wednesday.
"We are ready to provide any kind of support to allow the operation of the pipeline," Mr Erdogan said.
To the anger of Baghdad, Ankara had allowed the Kurds to open an alternative oil export pipeline through its territory.
