In response to last month's illegitimate referendum, the Iraqi armed forces in recent days have been deployed in Kirkuk and other disputed areas following the withdrawal of pro-KRG Peshmerga forces.
The operation was carried out with minimal casualties as Kurdish forces pulled back, but fears of an outbreak of clashes prompted the UN Security Council to call on Wednesday for all sides to "refrain from the threat and use of force, and to engage in constructive dialogue as a pathway to de-escalation".
An Iraqi court has ordered the arrest of the vice-president of the Kurdistan Region for calling troops sent to Kirkuk this week "occupying forces".
Mr Rasul said the territorial losses represented a "new Anfal for Kurdistan" - a reference to the campaign of genocide against Iraqi Kurds by Saddam Hussein's regime in 1987 and 1988.
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People living in areas under Kurdish control overwhelmingly backed secession but Iraqi Prime Minister Haider al-Abadi declared the vote illegal.
Tensions are escalating between Baghdad and the region of Kurdistan after the Kurds held a controversial referendum on the independence of the Kurdistan region and the disputed areas. Turkish president Recep Tayyip Erdogan said his country may shut its border with northern Iraq "at any moment" after earlier closing its air space to the region, Hurriyet newspaper reported on Thursday.
Iraq's central government and neighboring Iran were also deeply opposed to the referendum, in which more than 90 percent voted for independence.
Secessionist ambitions, however, convinced Iraq they needed to push the Peshmerga out of the territory, and despite the Kurdish paramilitary force having a lot of US-provided arms, they don't appear to have been willing to directly contest the offensive, at least not so far.