TEHRAN -  Iraqi Prime Minister Haider al-Abadi, whose forces Thursday battled militants in the west of the country and Kurds in the north, won the support of Iran's supreme leader at talks in Tehran.

Ayatollah Ali Khamenei "gave his support for measures taken by the Iraqi government to defend the unity, sovereignty and territorial integrity of Iraq", Khamenei's office said in a statement after their meeting.

Abadi also held talks earlier with Iran's President Hassan Rouhani. Buoyed by the success of Iraq's separate campaign against the Islamic State (IS) militant group, Abadi has been on a regional tour that on Wednesday saw him in Ankara. The Tehran stop came as Iraqi forces launched a new assault on Kurdish forces in a disputed area of Nineveh province, sparking heavy artillery exchanges, according to Kurdish authorities and correspondents in the region.

Government forces have since last week asserted control over thousands of square kilometres (miles) of territory long disputed with the Kurds, in a feud which has boiled over since a Kurdish independence referendum held in defiance of Baghdad on September 25.

The vote organised by the leadership of autonomous Iraqi Kurdistan in the country's north also angered neighbours Turkey and Iran, both fearful of anything that might stoke separatist sentiment among their own large Kurdish minorities.

Also on Thursday, federal troops and allied paramilitaries launched an offensive up the Euphrates Valley towards the Syrian border in a bid to retake the last IS bastion in Iraq.

Tehran has poured significant resources into the war against the militants in Iraq, providing weapons, advice and training to the Shia militias which dominate the paramilitary force.

Its involvement has irked Washington but has been defended by the Iraqi prime minister, who gave a firm rebuff to US Secretary of State Rex Tillerson over his comments on the issue.

Meanwhile, Baghdad on Thursday dismissed an offer from Iraqi Kurdish leaders to freeze the outcome of a vote for independence last month in a bid to pave the way for dialogue.

A spokesman for Prime Minister Haider al-Abadi said the referendum had already been consigned to history by facts on the ground after Iraqi federal troops and allied militia overran thousands of square kilometres (miles) of disputed territory long claimed by the Kurds.

"They speak of freezing the referendum but our answer is this - the referendum belongs to the past and we have finished with it on the ground," Abadi's chief spokesman Haidar Hamada said on Facebook. Iraqi Kurdish leaders offered on Wednesday to freeze the outcome of the September 25 vote which delivered a resounding yes to independence, in a bid to ease the crisis in their relations with Baghdad.

The proposal came as world powers scrambled to avert any further escalation of the conflict between the key allies in the fight against the Islamic State group that has seen more than 30 combatants killed.

There had been no immediate response from Baghdad but the Hashed al-Shaabi (Popular Mobilisation) force, whose mainly Iran-trained Shia paramilitaries played a major role in the operation against the Kurds, said a freeze did not go far enough and demanded the outright annulment of the independence referendum.

Iraqi troops attacked the Islamic State group's last bastion in the country on Thursday as the retreating militants battled to save their self-styled "caliphate" from total collapse. The launch of the keenly awaited offensive that the US-led coalition fighting IS 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 that the bitter dispute that has raged between the Baghdad government and Iraqi Kurdish leaders since they 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 that have been bastions of insurgency since soon after the US-led invasion of 2003. Iraqi forces have retaken more than 90 percent of the territory IS seized in the country in 2014, with the militants now confined to a small stretch of the valley adjoining some of the last areas they still hold in Syria.

"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 in a statement 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 told AFP that government forces were advancing on four fronts - from the east, southeast, north and south.

He said that units of the federal police and the elite Counter-Terrorism Service as well as the paramilitary Hashed al-Shaabi (Popular Mobilisation) force were supporting the army.

The Joint Operations Command said that by early afternoon government forces had recaptured several military bases southeast of Al-Qaim, including an airbase.

Crucially for an offensive in an overwhelmingly Sunni Arab region, Sunni tribal volunteers in the Hashed were heavily engaged alongside the Iran-trained Shia militias that are its mainstay.

The US-led coalition said it had carried out some 15 strikes on IS targets in and around Al-Qaim and the town of Albu Kamal on the Syrian side of the border.

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 IS's last stand in its ambitions of territorial control of the cross-border 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 militants from their stronghold in the north.

The launch of the offensive against IS's last Iraqi redoubt comes with federal troops and militia engaged in an operation to reassert central government control over thousands of square kilometres (miles) 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, 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.

Abadi, whose stock has been massively boosted by the success of the fightback against IS, was in Tehran for talks a day after holding meetings in Ankara.

On Thursday, his forces launched a new assault on Kurdish forces in the disputed oil-rich Zummar area of Nineveh province, Kurdish authorities said.

An AFP correspondent reported heavy artillery exchanges as Kurdish forces put up fierce resistance.

Parts of Nineveh province north and east of Iraq's second city Mosul are some of the last areas that Kurdish forces still hold outside their longstanding three-province autonomous region.

Thursday's assault was close to the route of a strategic oil export pipeline linking the Kirkuk fields retaken from the Kurds with the Turkish Mediterranean port of Ceyhan that fell into disuse during IS's lightning sweep through northern and western Iraq in 2014.

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," Erdogan said.

The course of the disused pipeline passes through the town of Faysh Khabur, near where the borders of Iraq, Turkey and Syria meet, in territory which lies undisputedly inside the autonomous Kurdish region.