BAGHDAD (Reuters) - U.S. Secretary of State Rex Tillerson urged the Iraqi government and the Kurdistan region on Monday to resolve their conflict over Kurdish self-determination and disputed territories through dialogue.

Tillerson laid out his position at the start of a meeting in Baghdad with Iraqi Prime Minister Haider al-Abadi, who in turn defended the role of an Iraqi paramilitary force backed by Iran against criticism the secretary of state made on Sunday.

“We are concerned and a bit sad,” Tillerson said in his opening remarks. “We have friends in Baghdad and friends in Erbil and we encourage all parties to enter into discussion ... and all differences can be addressed,” he said, referring to the Iraqi and Kurdistan region capitals.

The U.S. administration sided with Abadi in rejecting the validity of the referendum held last month in the Kurdish region, which produced an overwhelming yes for Kurdish independence.

The administration also called on the two sides to avoid further escalation, after Abadi retaliated against the vote by isolating the Kurdistan region and ordering his troops to seize the oil city of Kirkuk from Kurdish fighters.

“We don’t want to enter into any battle against any Iraqi component,” Abadi said. “When we entered Kirkuk we sent a clear message that the citizens of Kirkuk are important to us.”

It was Tillerson’s second meeting with Abadi in as many days. After Sunday’s meeting, alongside Saudi Arabia’s King Salman, Tillerson said it was time for Iranian-backed militias that had helped Baghdad defeat Islamic State to “go home”.

U.S. Secretary of State Rex Tillerson smiles alongside Qatar's Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani during a media availability after their meeting, in Doha, Qatar October 22, 2017. REUTERS/Alex Brandon/Pool

Abadi told Tillerson the paramilitary force called Popular Mobilisation “is part of the Iraqi institutions,” rejecting accusations that it is acting as Iran’s proxies.

“Popular Mobilisation fighters should be encouraged because they will be the hope of country and the region,” he said.

A few hours earlier, Abadi’s office published a statement rejecting Tillerson’s comments. “No party has the right to interfere in Iraqi matters,” it said [nL8N1MY1UJ].

Washington, which also backed Baghdad against Islamic State, is concerned Iran will use its increased presence in Iraq, and in Syria where it supports President Bashar al-Assad, to expand its influence in the region.

Shi’ite Muslim Iran’s influence in Iraq, where the population is also predominantly Shi’ite, has grown since the U.S. invasion of 2003 that overthrew dictator Saddam Hussein, a Sunni.

Iraq’s Sunni Muslim neighbours, including Saudi Arabia, share Washington’s concern about rising Iranian influence.

Tehran has trained and armed the Iraqi Popular Mobilisation forces that have fought, often alongside Iraqi government units, against Islamic State, which was effectively defeated in July when a U.S.-backed offensive captured its stronghold, Mosul.

The United States has over 5,000 troops deployed in Iraq and provided critical air and ground support in the offensive on Islamic State. It is also the main backer of the Kurdish-led Syrian coalition that captured the IS stronghold of Raqqa earlier this month.

Of the closest groups to Iran within Popular Mobilisation, Asaib Ahl al-Haq, reacted to Tillerson’s comment by saying it would be the Americans who will be forced to leave Iraq.

“Your forces should get ready to get out of our country once the excuse of Daesh’s presence is over,” said Asaib’s leader, Sheikh Qais al-Khazali, according to the group’s TV channel, al-Aahd.