Thousands of residents fled Kurdish districts, heading in buses and cars towards the autonomous Kurdistan region of northern Iraq. A resident of Kirkuk said today that ethnic Turkmen were firing guns into the air in celebration of the takeover by government forces.
United States officials said they were "engaged with all parties in Iraq to de-escalate tension".
Baghdad's tough line, ruling out talks sought by the Kurds unless they renounce the breakaway move, is backed by neighbors Turkey and Iran - both with their own sizeable Kurdish minorities, and in Turkey's case, a long-running Kurdish insurgency.
Fighting between Baghdad and the Kurds could open an entirely new front in Iraq's 14-year-old civil war and potentially draw in regional powers such as Turkey and Iran. The Associated Press reported that Kurdish fighters had abandoned their positions outside Kirkuk's airport while civilians were fleeing the city, where sporadic gunfire could be heard. Kurds consider it the heart of their homeland; they say it was cleansed of Kurds and settled with Arabs under Saddam to secure control of the oil that was the source of Iraq's wealth.
He said Iraqi forces have "burnt lots of houses and killed many people" south of the disputed city.
Iraqi oil industry officials said there was no disruption to production from the facilities of the North Oil Company, which is based in Kirkuk and one of the two main oil companies that together provide almost all of Iraq's government revenue.
The Kurdistan Region Security Council later released a statement that said Peshmerga fighters had destroyed at least five armoured vehicles belonging to the state-sanctioned Shia militias following the attack, resulting in what an Iraqi-Kurdish commander referred to as "lots of casualties".
"Everybody stay focused on defeating ISIS".
The action in Iraq helped spur a jump in world oil prices on Monday.
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Baghdad insisted the city and its province be returned, but matters came to a head when the Kurdish authorities expanded their referendum to include Kirkuk. "Our fearless forces will regain control of all Kirkuk oilfields and then we will restart production immediately".
Iraq's Joint Operations Command (JOC), which groups all pro-government forces, did not specify whether there had been significant clashes in the operation, but the speed of the advance suggested Kurdish fighters were so far withdrawing without resistance.
The Kurdish secession bid was strongly opposed by neighbours Iran and Turkey.
The peshmerga are, in turn, divided between two parties, the Patriotic Union of Kurdistan (PUK) and Kurdish President Masoud Barzani's Kurdistan Democratic Party (KDP).
Both Kurdish parties control their own Peshmerga units.
The PUK had supported a UN-backed plan for negotiations with Baghdad in exchange for dropping the referendum.
Baghdad described the advance as largely unopposed, and called on the Peshmerga to co-operate in keeping the peace. "We are aware of reports of a limited exchange of fire during the predawn hours [today], and we believe this to have been an isolated incident", he said of media reports of fighting between Iraqi and Kurdish fighters.
During the years of U.S. occupation that followed, Washington leaned on its Kurdish allies to keep their ambitions in check to avoid triggering another war amid an insurgency by Sunni Arabs.
The skirmish between forces that fought together to oust Islamic State militants from their stronghold of Mosul in a brutal operation presented a major distraction for Iraqi forces, which had begun mobilizing westward for operations against the group in the last pockets it controls near the Syrian border. But the vote angered neighbours and put pressure on Abadi to act. The Iraqi military said it seized two major oil fields outside the city.
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