US Secretary of State Rex Tillerson on Monday flew in to Baghdad on a surprise visit for talks with Iraq's Prime Minister Haider al-Abadi and President Fuad Massum.

The visit, during which Tillerson and Abadi will hold their second meeting in as many days, comes after America's US top diplomat called on Iranian militias to leave Iraq, prompting a sharp response from the Iraqi cabinet.

"Certainly Iranian militias that are in Iraq, now that the fighting against (the Islamic State group) is coming to a close, those militias need to go home," Tillerson said Sunday at a press conference in Riyadh.

But Iraq's cabinet on Monday insisted that the paramilitary forces that helped it to defeat IS were fully Iraqi.

"The fighters of the Hashed (al-Shaabi paramilitary units) are Iraqis who are concerned for their country and have sacrificed for its defence and for its people," it said in a statement, quoting a source close to Abadi.

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.

On the crisis between Baghdad and Iraqi Kurdistan, the US State Department on Friday called for Iraqi federal forces to limit their "movements" in areas disputed by the two sides to avoid more violence.

Iraqi forces clashed with Kurdish units in the northern province of Kirkuk last week, in an operation that saw them retake swathes of disputed territory from the Kurds.

Both federal and Kurdish forces have been key US allies in the war against IS.

"In order to avoid any misunderstandings or further clashes, we urge the central government to calm the situation by limiting federal force movements in disputed areas," State Department spokeswoman Heather Nauert said.

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 visits to Saudi Arabia and Qatar.

Source: AFP