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.
Meanwhile, reports say a militia backed by the Baghdad government has taken control of the town of Sinjar in the north-western Nineveh province.
The takeover happened without violence after Kurdish Peshmerga soldiers withdrew from the area, the reports added.
Kirkuk is an oil-rich province claimed by both the Kurds and the central government. It is thought to have a Kurdish majority, but its provincial capital has large Arab and Turkmen populations.
Kurdish Peshmerga forces took control of much of the province in 2014, when Islamic State (IS) militants swept across northern Iraq and the Iraq army collapsed.
The Iraqi parliament asked Mr Abadi to deploy troops to Kirkuk and other disputed areas after the referendum result was announced, but he said last week that he would accept them being governed by a “joint administration” and that he did not want an armed confrontation.
On Sunday, his cabinet accused the KRG of deploying non-Peshmerga fighters in Kirkuk, including members of the PKK, which it said was tantamount to a “declaration of war”. But KRG officials denied this.