BAGHDAD (NYTIMES) - Secretary of State Rex W. Tillerson slipped into Iraq Monday night (Oct 23) after having spent the morning in Afghanistan, but his welcome in Baghdad was far less effusive as the Trump administration pushes to isolate Iran, an important Iraqi ally.

The diplomatic challenges for the United States in Iraq have become a minefield of competing interests as the Islamic State in Iraq and Syria (ISIS) surrenders the last of its Iraqi territory and a host of squabbling groups fight to fill the vacuum.

After meeting with Prime Minister Haider al-Abadi of Iraq, Tillerson called for unity in the country, long troubled by sectarian and tribal divisions.

Last week, the Iraqi military seized Kirkuk, wresting the contested city from Kurdish forces, which control much of the northern third of the country. Both sides in the struggle for Kirkuk have been crucial US allies in the fight against ISIS.

"We are concerned and have been saddened by the recent differences that have emerged between the Kurdistan regional government and the Iraqi central government," Tillerson said in statements made to reporters after he had met with al-Abadi.

Asserting that "we have friends" in Baghdad and the Kurdish region's capital, Irbil, Tillerson said "we encourage both parties to enter into discussion and dialogue". Hours before Tillerson arrived, al-Abadi's office released a testy statement rejecting Tillerson's call the previous day for Iranian-backed militias - known as popular mobilisation forces or Hashad al-Shaabi - to either disband or leave Iraq.

Although the militias may be armed and trained by Iran, the militia members are Iraqis.

"We wonder about the statements attributed to the American secretary of state about the popular mobilisation forces," the statement from the prime minister's office said.

The militias were recruited and integrated into the Iraqi military in 2014 after ISIS militants swept through parts of Iraq and seized nearly a third of the country despite years of effort and billions of dollars spent by the United States to train government forces.

Members of the militias are Iraqi patriots who "have sacrificed greatly to defend their country," al-Abadi's statement said. "No side has the right to intervene in Iraq's affairs or decide what Iraqis should do."