Iraqi government forces have entered central Kirkuk after taking key installations outside the disputed city from Kurdish fighters.
Thousands of people fled the city ahead of the Iraqi advance.
The Iraqi military 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 25 September vote.
While Kirkuk is outside Iraqi Kurdistan, Kurdish voters in the city were allowed to take part.
Iraq's prime minister, Haider al-Abadi, had denounced the vote as unconstitutional. But the Kurdistan Regional Government (KRG) insisted it was legitimate.
US officials said they were "engaged with all parties in Iraq to de-escalate tension".
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Mr Abadi said in a statement on Monday that the operation in Kirkuk 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 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.
On Monday, the Iraqi military said its units had taken control of the K1 military base, the Baba Gurgur oil and gas field, and a state-owned oil company's offices.
Thousands of people fled the city ahead of the Iraqi advance.
The Iraqi military 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 25 September vote.
While Kirkuk is outside Iraqi Kurdistan, Kurdish voters in the city were allowed to take part.
Iraq's prime minister, Haider al-Abadi, had denounced the vote as unconstitutional. But the Kurdistan Regional Government (KRG) insisted it was legitimate.
US officials said they were "engaged with all parties in Iraq to de-escalate tension".
Skip Twitter post by @RudawEnglish Report
End of Twitter post by @RudawEnglish
Mr Abadi said in a statement on Monday that the operation in Kirkuk 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 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.
On Monday, the Iraqi military said its units had taken control of the K1 military base, the Baba Gurgur oil and gas field, and a state-owned oil company's offices.

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