Iraqi Prime Minister Haider al-Abadi met top US diplomat Rex Tillerson in Baghdad, challenging the secretary of state over his comments on Iranian militias in Iraq.

Tillerson, in Riyadh on Sunday, had called on Iranian militias in Iraq to "go home" as the fight against the Islamic State group was ending. His comments prompted a sharp response from Baghdad. "The fighters of the Hashed al-Shaabi are Iraqis who have fought terrorism, defended their country and made sacrifices to defeat (IS)," Abadi said yesterday, according to a statement from his office.

The 60,000-strong Hashed was formed in 2014 after IS seized swathes of northern Iraq, routing government forces. A coalition mostly made up of Iranian-backed militias, it has played a key role in Iraq's successful fight against the jihadists in the past three years.  The group answers to the prime minister's office and parliament has voted to integrate it into state forces.

"The Hashed is an institution that depends on the Iraqi state and the constitution does not allow the presence of armed groups outside the law," Abadi said. But experts say regular visits to Iraq by Iran's Major General Qassem Soleimani, commander of its Revolutionary Guards' foreign arm, the Quds Force, reflect Tehran's influence in the country.

Iraq's cabinet on Monday insisted the paramilitary forces that helped it to defeat IS were fully Iraqi. The cabinet added that "nobody has the right to interfere in Iraqi affairs."  Abadi and Tillerson both attended a landmark meeting between Saudi and Iraqi leaders in Riyadh on Sunday aimed at upgrading strategic ties between the two countries and countering Iran's regional influence.

Tillerson and Abadi, in Baghdad, discussed "government measures taken to restore the authority of the federal government in Kirkuk," Abadi's spokesman Haydar Hamada said.

Last week, central government forces wrested back control of the disputed oil-rich province from Kurdish forces in a sweeping operation after a controversial Kurdish independence vote.

"We are concerned and a bit saddened by the recent differences that have emerged between the Kurdistan Regional Government and the Iraqi central government," Tillerson said. "We are -- we have friends both in Baghdad, and we have friends in Arbil, and we encourage both parties to enter into discussion and dialogue."

The US State Department had on Friday called for Iraqi federal forces to limit their "movements" in areas disputed by the two sides to avoid more violence. Both federal and Kurdish forces have been key US allies in the war against IS.

On Sunday, as calm returned to the areas in northern Iraq, federal and paramilitary forces said they lost five men in the clashes, adding to 26 deaths reported on the Kurdish side. The Iraqi operation to retake disputed territories came three weeks after a Kurdish independence referendum condemned as illegal by Baghdad and criticised by Washington.

Before flying to Baghdad, Tillerson earlier on Monday also made a previously unannounced trip to Afghanistan, following the visits to Saudi Arabia and Qatar.