The US has called for “calm” after Iraqi government forces seized the northern city of Kirkuk and key installations from Kurdish control.
State Department spokeswoman Heather Nauert urged all parties to “avoid further clashes”.
Iraqi soldiers moved into Kirkuk three weeks after the Kurdistan Region held a controversial independence referendum.
They are aiming to retake areas under Kurdish control since Islamic State militants swept through the region.
Residents of Kurdish-controlled areas, including Kirkuk, overwhelmingly backed secession from Iraq in a vote on 25 September.
While Kirkuk is outside Iraqi Kurdistan, Kurdish voters in the city were allowed to take part.
Iraqi Prime Minister Haider al-Abadi had denounced the vote as unconstitutional. But the Kurdistan Regional Government (KRG) insisted it was legitimate.
In a statement on Monday, Ms Nauert said Washington was “very concerned by reports of violence around Kirkuk”.
“We support the peaceful exercise of joint administration by the central and regional governments, consistent with the Iraqi constitution, in all disputed areas.”
Ms Nauert said the US was working with officials from all parties to “encourage dialogue”, warning that “there is still much work to be done to defeat Isis (Islamic State) in Iraq”.
Earlier, President Donald Trump said US officials were “not taking sides”.
“We don’t like the fact that they’re clashing,” he added.
Senator John McCain, who heads the Senate Armed Services Committee, warned the Iraqi government of “severe consequences” if US-supplied weaponry was misused in operations against Kurdish forces.
“The United States provided equipment and training to the government of Iraq to fight (Islamic State) and secure itself from external threats – not to attack elements of one of its own regional governments.” he said. (Courtesy BBC)