The offensive, which follows weeks of soaring tensions between two US allies in the battle against the Islamic State group, aims to retake oil and military sites that Kurdish forces took over during the fightback against the jihadists.
Thousands of residents were seen fleeing Kurdish- controlled Kirkuk city, according to an AFP journalist.
Iraqi and Kurdish peshmerga forces exchanged artillery fire early today south of the capital of the oil-rich province, after the launch of the operation overnight which triggered a spike in oil prices on world markets.
Iraq's Joint Operations Command said its forces had retaken the K1 military base northwest of Kirkuk, the military airport east of the city and the Baba Gargar oil field, one of six in the disputed region.
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The operation follows an armed standoff between Kurdish forces and the Iraqi army prompted by the September 25 non- binding referendum that produced a resounding "yes" for independence for the autonomous Kurdish region of northern Iraq.
Baghdad has declared the vote -- held despite international opposition -- illegal.
Iraqi Prime Minister Haider al-Abadi said the operation was necessary to "protect the unity of the country, which was in danger of partition" because of the referendum.
"We call upon all citizens to cooperate 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 said.
Multiple peshmerga fighters were injured in the initial clashes and hospitalised in Kirkuk, a local security source said.
But peshmerga forces loyal to the Patriotic Union of Kurdistan (PUK), a political party linked to Iraqi President Fuad Masum, who is himself a Kurd, were later reported to be withdrawing from areas under their control.
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.
Iraq's National Security Council yesterday said it viewed as a "declaration of war" the presence of "fighters not belonging to the regular security forces in Kirkuk", including fighters from Turkey's outlawed Kurdistan Workers' Party (PKK).
For their part the Iraqi forces have said they have no wish to enter Kirkuk but that they wish to retake military positions and infrastructure which were under their control before their troops withdrew in the face of hostility from the jihadists.
On the fringes of the town, they used loudspeakers to call on the peshmerga to give up their positions, local sources said.
Polling during the referendum was held not only in the three provinces of the autonomous Kurdish region but also in adjacent Kurdish-held areas, including Kirkuk, that are claimed by both Baghdad and Iraqi Kurdistan.
The Kurds 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.
The fields would provide crucial revenue to Baghdad, which has been left cash-strapped from the global fall in oil prices and three years of battle against IS.
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