The Iraqi government dismissed a call from USinfo-icon Secretary of State Rex Tillerson for Iranian-backed paramilitary units that helped Baghdadinfo-icon defeat Islamic Stateinfo-icon and capture the Kurdish-held city of Kirkuk to end operations in Iraqinfo-icon.

The paramilitary units have been expanding their reach to northern Iraq, supporting government forces which seized the Kurdish-held city of Kirkuk one week ago in a lightning advance in retaliation for a referendum on independence.

Iraqi forces are deploying tanks and artillery just south of a Kurdish-operated oilinfo-icon pipeline that crosses into Turkeyinfo-icon, a Kurdish security official said, the latest in a series of Iranian-backed operations against the Kurds.

Speaking after a meeting on Sunday with Iraqi Prime Minister Haider al-Abadi and Saudi Arabiainfo-icon's King Salman, Tillerson said it was time for the Iraqi Popular Mobilisation forces and their Iranian advisers to "go home".

Washington is concerned Iraninfo-icon will use its expanded presence in Iraq and in Syriainfo-icon to expand its influence in the region. But Abadi showed unwillingness to meet Tillerson's demand.

"No party has the right to interfere in Iraqi matters," a statement from his office read. It did not cite the prime minister himself but a "source" close to him.

Predominantly Shiainfo-icon Iran and its Sunni rival Saudi Arabia are locked in a proxy warinfo-icon for influence in the Middle Eastinfo-icon.

The international battle against the militant Islamic State group in northern Iraq since 2014 saw the United Statesinfo-icon and Iran effectively fighting on the same side, with both supporting the Iraqi government against the militants.

Washington has 5,000 troops in Iraq, and provided air support, training and weaponsinfo-icon to Iraqi government forces, even as Iran armed, trained and advised the Shia paramilitaries which often fought alongside the armyinfo-icon.

But the latest twist in the Iraq conflictinfo-icon, pitting the central government against the Kurds, is trickier for US policymakers. Washington still supports the central government but has also been allied to the Kurds for decades.

Iran exhibited its sway over Baghdad's policies during tensions over a referendum last month in which the semi-autonomous Kurdistan region voted to secede from Iraq against Baghdad's wishes, Kurdish officials say.

Baghdad responded to the vote by seizing the oil city of Kirkuk, which the Kurds see as the heart of any future homeland.

Major-General Qassem Soleimani, commander of foreign operations for Iran's elite Revolutionary Guards, repeatedly warned Kurdish leaders to withdraw from Kirkuk or face an onslaught by Iraqi forces and allied Iranian-backed fighters, Kurdish officials briefed on the meetings said.

Iraq's Sunni neighbours, including Saudi Arabia, share Washington's concerns over Shia power Iran's influence in Iraq, where the population is predominantly Shia.

The office of Abadi, himself a Shia, said the paramilitary forces were under the authority of the Iraqi government. "Popular Mobilisation are Iraqi patriots," it said in the statement.

Iran's Foreign Minister Mohammad Javad Zarif also rejected Tillerson's statement.

The paramilitaries could not go home because "they are at home" already, he was quoted as saying by the state news agency IRNA.