Iraqi Prime Minister Haider al-Abadi has rejected a call by Washington for Iranian-backed fighters to leave Iraq at a meeting with US Secretary of State Rex Tillerson in Baghdad.

Tillerson made the unannounced visit to the Iraqi capital on Monday came amid heightened tensions between the two countries over the role of the Popular Mobilisation Forces (PMF), Shia paramilitaries that helped defeat ISIL in Iraq.

The top US diplomat had previously called for Iraq-based "Iranian militias ... to go home" as the fight against ISIL "is coming to a close".

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But Abadi insisted on Monday that the force consists solely of Iraqi nationals who "fought terrorism" and made sacrifices that contributed to the victory over the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) armed group.

Calling it "part of the Iraqi institutions," Abadi said PMF fighters "should be encouraged because they will be the hope of country and the region", according to a statement by his media office.

Javad Zarif, Iran's foreign minister, waded into the debate, tweeting on Monday: "Exactly what country is it that Iraqis who rose up to defend their homes against ISIS return to?"

Exactly what country is it that Iraqis who rose up to defend their homes against ISIS return to? Shameful US FP, dictated by petrodollars. — Javad Zarif (@JZarif) October 22, 2017

Tillerson's visit to Baghdad came a few days after the Iraqi army, backed by the PMF, claimed control of all of oil-rich Kirkuk province after it captured Altun Kupri town following intense fighting with Kurdish Peshmerga forces.

Baghdad's forces had previously captured Kirkuk city, as part of a major military operation in the wake of a controversial September 25 referendum on Kurdish secession that Baghdad had declared illegal.

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Al Jazeera's Stefanie Dekker, reporting from Erbil, the capital of the Kurdish Regional Government in northern Iraq, said the issue of PMF's role is complicated to resolve for a number of reasons.

"They have different command structure although they fall under the commander in chief, who is Abadi. This issue is also closely linked to curtailing the growing Iranian influence in the region," she said.

"We know that the Americans want to resolve the conflict between Kurds and Baghdad through dialogue," said Dekker.

"They are going to be keen to push forward some sort of timeframe to solve disputed territory issue," she added.

Tillerson and Abadi, along with Saudi King Salman, also participated in the inaugural meeting of the Saudi Arabia-Iraq Coordination Committee in Riyadh on Sunday.

Earlier on Monday, before meeting Abadi for the second time in two days, Tillerson flew from Qatar to Afghanistan's Bagram Air Base, where he met President Ashraf Ghani and other Afghan leaders.