Overnight Iraqi national army on Sunday took control of Kirkuk's industrial district, as well as the city's oil refinery before going on the move, reportedly without any opposition from Kurdish Peshmerga militia that had controlled the area since the collapse of Islamic State (ISIL) despite it being outside of their semi-autonomous region.
He did so by holding a referendum on Kurdish independence on 25 September that was greeted with enthusiasm by Iraqi Kurds.
Washington called for calm on both sides, seeking to avert an all-out conflict between Baghdad and the Kurds that would open a whole new front in Iraq's 14-year-old civil war and potentially draw in regional powers such as Turkey and Iran.
After the deadline expired, Abadi accused the Kurds of deploying militiamen from the Kurdistan Workers' Party, or PKK, a faction that has waged battles for autonomy in Turkey's Kurdish region for decades.
"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.
The crisis is raising fears of fresh chaos in Iraq just as the country's forces are on the verge of routing the Islamic State group from the last territory it controls in the country.
The government in Baghdad said the Peshmerga had withdrawn "without fighting".
Oil-rich Kirkuk is claimed by both the Kurdish Regional Government and Baghdad.
The withdrawal of part of the Kurdish forces is ultimately a reflection of deep divisions between the Kurdish leaders and their parties, whose rivalry has always been intense.
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A resident inside Kirkuk said members of the ethnic Turkmen community in the city of 1-million people were celebrating, driving in convoys with Iraqi flags and firing shots in the air. Kurds consider it the heart of their homeland; they say it was cleansed of Kurds and settled with Arabs under Saddam to secure control of the oil that was the source of Iraq's wealth.
Baghdad described the advance as largely unopposed, and called on the Peshmerga to co-operate in keeping the peace.
He said Iraqi forces have "burnt lots of houses and killed many people" south of the disputed city.
The Kurdish regional government did not initially confirm the Iraqi advances, but Rudaw, a major Kurdish TV station, reported that Peshmerga had left positions south of Kirkuk.
Kurdish forces, who were key allies in the US-backed offensive against IS, are refusing to surrender positions they took during the fightback against the jihadists over the past three years.
The "government of Abadi bears the main responsibility for triggering war on the Kurdistan people, and will be made to pay a heavy price", the Peshmerga command said in a statement, cited by Kurdish leader Barzani's assistant Hemin Hawrami.
The PUK had supported a UN-backed plan for negotiations with Baghdad in exchange for dropping the referendum.
The skirmish between forces that fought together to oust Islamic State militants from their stronghold of Mosul in a brutal operation presented a major distraction for Iraqi forces, which had begun mobilizing westward for operations against the group in the last pockets it controls near the Syrian border.
During the years of US occupation that ensued, Washington leaned on its Kurdish allies to keep their ambitions in check to avoid triggering another war amid an insurgency by Sunni Muslim Arabs.
Barzani said the time had come for an independence referendum.
Baghdad and the Kurds have long-running disputes over oil exports, extraction and sharing oil revenues.