"Their intention is to enter the city and take over (the) K1 base and oil fields", it said in a post on Twitter.
A local official in charge of the displaced said tens of thousands, mostly Kurds, were heading out of the city, although at the same time crowds on the streets of Kirkuk's southern outskirts welcomed Iraqi forces.
Tension has steadily mounted between Baghdad and the Erbil-based KRG since September 25, when Iraqis in KRG-controlled areas - and in several disputed territories, including Kirkuk - voted on whether or not to declare political independence.
The Kurdistan Workers' Party (PKK), which has fought a more-than-three-decade-long insurgency against Turkey, also has forces deployed in Kirkuk in support of the PUK.
Elite Iraqi security forces have captured the Kurdish government headquarters buildings in the centre of Kirkuk with the Iraqi Prime Minister Haider al-Abadi ordering the Iraqi flag to be raised over Kirkuk and other disputed territories.
US Senator John McCain commented on the recent situation around Kirkuk in northern Iraq after clashes between the government forces and Kurdish Peshmerga troops earlier this day. Washington has called for "all parties to immediately cease military action and restore calm", adding that Isis remained the true enemy of all parties in Iraq and they should focus on its elimination. The Kurdish Rudaw news service said at least seven Iraqi militiamen were killed south of Kirkuk, citing an unidentified peshmerga commander.
Moreover, the U.S. senator underscored that Iraqi Prime Minister Haider al-Abadi and the Kurdish Regional Government should begin talks about Kurdish independence from Iraq at an appropriate time.
The referendum had faced strong opposition from most regional and worldwide actors (including the U.S., Turkey and Iran), who warned that the poll would distract from Iraq's fight against terrorism and further destabilize the already-volatile region.
There were clashes between Kurdish and Shi'ite Turkmen groups in another city, Tuz Khormatu, about 75 km (47 miles) south of Kirkuk, but no casualties were reported.
Kirkuk, a multi-ethnic city with a large Kurdish community, shaped up as a flashpoint as it is claimed by both sides.
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.
It remains unclear how far Iraq's army and its militia partners intend to advance, but the importance of Kirkuk and the complexity of the armed alliances increase the "potential for political and military miscalculations", said Glen Ransom, Iraq analyst at Control Risks in Dubai.
The action in Iraq helped spur a jump in world oil prices on Monday.
The US has been closely allied to the Kurds in Iraq and Syria, but strongly opposed the independence referendum which it saw as provocative and divisive. Early Monday Iraqi forces began moving to evict Kurds from a military base and oil fields. Representatives of both parties were taking part in the talks.
The peshmerga forces based in Kirkuk are mainly loyal to Masum's Patriotic Union of Kurdistan (PUK) of party, a rival of Barzani's Kurdistan Democratic Party (KDP).
The status of Kirkuk and fate of the Kurds were left unsettled 14 years ago when a US-led invasion toppled Saddam.
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".
During the years of USA 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.
"This is the result of disobedience of Masoud Barzani", said the Iraqi fighter who was filming, referring to the leader of Iraqi Kurdistan and the KDP.
Turkey, which had developed a good working relationship with the Iraqi Kurds and let the landlocked region export oil through its pipes, has swung behind Baghdad, furious at a secession bid that might ignite similar demands from its own Kurds.