According to security forces, troops moved into the building with no opposition from Kurdish Peshmerga fighters.
A dozen Humvees from Iraq's US-trained Counterterrorism Service arrived at the building and took position in the vicinity, alongside the local city police.
There was no immediate comment from Kurdish authorities.
The advance was part of a major operation to retake the oil-rich province, amid an escalating dispute in the wake of a controversial September 25 referendum on Kurdish secession that Baghdad had declared illegal.
The Iraqi army said on Monday it has seized control of the city's airport, in addition to an oil field, the strategic K1 military base and the Taza Khormatu district southeast of Kirkuk.
As the Iraqi army advanced, thousands of people, including civilians and Peshmerga fighters, fled the disputed city.
Kurdish forces had previously vowed to defend Kirkuk, and for three days they were locked in an armed standoff with Iraqi government troops and allied Iranian-backed paramilitaries known as Popular Mobilisation Forces (PMF) on the outskirts of the city.
"It seems to be a complete withdrawal from the Peshmerga inside and around the city," Al Jazeera's Charles Stratford, reporting from Erbil, said.
"There is going to be a lot of soul-searching, questioning and anger among the Kurdish Regional Government (KRG) about exactly how this happened after such a strong rhetoric for days now, that the Kurds remained united and that they would defend Kirkuk at all cost."
Kurdish Peshmerga forces took control of oil-rich Kirkuk after the Iraqi army fled from a major offensive by the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group in 2014.
Since then, there has not been an agreement between the KRG and the federal government in Baghdad about who should control the area - and benefit from its vast oil wealth.
Tensions between the two sides have been running especially high since Iraqi Kurds overwhelmingly voted for secession in last month's referendum.
The non-binding poll was held in areas under control of the KRG and in a handful of disputed territories, including Kirkuk.
Shortly after the referendum, the Iraqi parliament asked Prime Minister Haider al-Abadi to send troops to Kirkuk and take back control of the region's oil fields.
Kirkuk province is one of Iraq's two main oil-producing regions, believed to have around four percent of the world's oil resources.
It lies outside the official borders of the Kurds' semi-autonomous territory and is home to Kurds, Arabs, Turkmen and Christians.
The vast majority of Turkmen and Arabs who have lived in Kirkuk for generations boycotted the referendum.
"There are many Kurds who call it their Jerusalem," said Stratford, "but there's also considerable opposition among the Arabs and the Turkmen about any idea with respect to Kirkuk being part of a future independent Kurdish state."
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