Iraqi state media says Iraqi forces have entered the disputed region of Kurdish-held Kirkuk, apparently without firing a shot.
Monday's Peshmerga statement accused a group within the PUK of "treason" for assisting Baghdad's advance.
Peshmerga fighters who were ordered to withdraw expressed frustration. He feared the referendum, guaranteed to alienate all the Kurds'allies, would turn out to a political error with similar calamitous consequences.
Tensions between the two sides have been running especially high since Iraqi Kurds overwhelmingly voted for secession in a September 25 referendum that Baghdad rejected as illegal.
McCain called for Kurdish and Iraqi leaders to "engage in a dialogue about the Kurdish people's desire for greater autonomy from Baghdad at an appropriate time and the need to halt hostilities immediately".
Both the central government and the Kurds share an interest in keeping oil flowing from northern Iraq, so markets would probably calm down quickly after any interruption in these exports, according to Manaar's Altaie.
Iraqi forces thrust into Kirkuk city, capital of the oil-rich province, and took control of the governor's office, which had been left deserted, the federal police chief said.
"We call upon all citizens to co-operate with our heroic armed forces, which are committed to our strict directives to protect civilians in the first place, and to impose security and order, and to protect state installations and institutions", he added.
He said Iraqi forces have "burnt lots of houses and killed many people" south of the disputed city. "IS remains the true enemy of Iraq, and we urge all parties to remain focused on finishing the liberation of their country from this menace". Kurdistan's regional government is heavily reliant on the field for its energy needs.
The conflict in Iraq helped spur a jump in world oil prices on Monday. The U.S. has armed, trained and provided vital air support to both sides in their shared struggle and called the frictions a distraction against the most important fight.
Pro-PUK forces were deployed south of the city, including at oil fields, while fighters loyal to the rival Kurdistan Democratic Party (KDP), linked to Iraqi Kurd leader Massud Barzani who initiated the referendum, were deployed to the north.
PUK officials on Sunday said that they had made an offer to Baghdad to agree to allow central government troops from the Presidential Guard, who are ethnically Kurdish, into the Kirkuk region.
Kurdish forces have been in control of six fields in the Kirkuk region providing some 340,000 of the 550,000 barrels per day exported by the regional administration. Representatives of both parties were taking part in the talks.
Part of the PUK, much divided since its leader Jalal Talabani suffered a stroke and sank into a coma, opposed the independence referendum as a manoeuvre by Mr Barzani to present himself as the great Kurdish nationalist leader.
"It's comical, really", said a Kurdish official with the KDP, talking about US silence given the presence of Iran-supported militias in the advance.
Although Iraqi officials portrayed the Kurds as retreating without a fight, Kurdish officials said Peshmerga clashed with the "Popular Mobilisation", Shiite forces trained and armed by Iran that operate alongside regular Iraqi troops.
Iraqi and peshmerga forces could be seen early on Sunday still facing off in positions on the outskirts of Kirkuk, though there were no signs of troop movements.
"The war on ISIS is edging to an end and now the real war starts, the war between the regional powers in order to control resources and define their own areas of influence", said Sami Nader, head of the Levant Institute for Strategic Affairs in Beirut.
The US-led task force said it was aware of "a limited exchange of fire during predawn hours", which it believed was "a misunderstanding and not deliberate as two elements attempted to link up under limited visibility conditions". For years, Turkey has notably described a unilateral move by the Kurds to control Kirkuk as a red line.
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