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.
They rejected what they described as "military threats" from Iraqi forces against Kurdish Peshmerga fighters, and pledged to defend Kurdish-held territory in case of an attack.
He did so by holding a referendum on Kurdish independence on 25 September that was greeted with enthusiasm by Iraqi Kurds. Controversially, the vote also included so-called disputed areas outside the KRG's official boundaries, including Kirkuk.
Almost 93 percent of voters chose independence in September's Kurdish referendum. Abadi's office said the militias would remain on the outskirts of Kirkuk rather than enter the city.
Following the referendum, Iraq's parliament demanded the military be deployed to Kirkuk to reassert control.
Following the Kurdistan Region's recent vote for independence, Iraqi Prime Minister Haider al-Abadi said the offensive was aimed at protecting "national unity". In response, the Iraqi central government shut down Kurdistan's worldwide airport and has threatened to close the region's borders with Iran and Turkey, which have warned of potential military action.
The situation in Kirkuk has always been described by analysts as a potential powder keg, while the risk of civil war between Baghdad and the Kurds has witnessed a notable increase in the wake of the referendum.
The two sides have been at loggerheads since the Kurds voted overwhelmingly for independence in the referendum last month that Baghdad rejected as illegal. On one side is the Iraqi army and allied Iranian-backed Shiite militia, known as the Popular Mobilization Units (PMU), and on the other side the Kurdish peshmerga.
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). An Iraqi Oil Ministry official said that it would be "a very short time" before the Iraqi military seized all the oilfields in Kirkuk province.
Iraq has since rebuilt its armed forces with considerable United States aid, and they are battle-hardened and flush with victory after driving IS from most of the territory it once held.
The status of Kirkuk and fate of the Kurds were left unsettled 14 years ago when a US-led invasion toppled Saddam. The Iranians have always been anxious about Iraqi Kurdistan becoming a base for USA forces that could be used against us.
Kirkuk's ethnic and religious mixture are a microcosm of Iraq's sectarian divide itself - sitting on top of Iraq's second largest oil reserves. Kurdish party headquarters inside Kirkuk had been abandoned.
Since the 2003 United States invasion of Iraq, Kurds have sought to tip the demographics of the province back in their favor.
The Iraqi military moved into Kirkuk three weeks after the Kurdistan Region held a controversial independence referendum.
The exodus in buses and cars towards Arbil and Sulaimaniyah, the two main cities of autonomous Iraqi Kurdistan, created traffic jams on roads leading out of Kirkuk. The city falls 32 kilometers (20 miles) outside the Kurds' autonomous region in northeast Iraq.
Peshmerga and the Iraqi army have cooperated against IS.
Al-Abadi's Cabinet said Sunday that fighters from Turkey's Kurdish insurgency, the PKK, were beginning to appear in Kirkuk, and declared that would be tantamount to an act of war.
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. Early Monday Iraqi forces began moving to evict Kurds from a military base and oil fields.
The oil fields are particularly contested. However, Kurdish politicians often complain they do not receive their fair share. Under the Iraq's constitution, the Kurds are supposed to receive 17 percent of Iraq's oil revenues.