"It is my constitutional duty to work for the benefit of the citizens and to protect our national unity that came under threat of fragmentation as a result of the referendum that was organized by the Kurdish region," Abadi said in a statement on Monday, Al Jazeera news channel reported.
"The referendum came at a time where the country is fighting against terrorism that has come in the form of ISIL. We tried to urge (the Kurds) not to violate the constitution and to focus on fighting ISIL, but they did not listen… They chose their personal interests over Iraq’s interests."
The prime minister further assured Kirkuk's residents that their safety was Iraq's priority, while calling on the Kurdish forces to align themselves with the federal army.
"And we are only performing our duty in keeping the city safe for Iraqis (of) various factions. We urge all citizens to cooperate with our heroic armed forces… in implementing security in the area.
"We call on the Peshmerga forces to perform their duties under the central command under the Iraqi armed forces."
The latest incidents come amid simmering tensions between the central government in Baghdad and the Kurdistan Regional Government (KRG) over a recent controversial referendum on the secession of the semi-autonomous Iraqi Kurdish region.
The plebiscite took place on September 25, sparking strong objection from Baghdad. Iraq’s neighbors and the international community also voiced concerns about the repercussions of the vote, which was only supported by Israel.
Kirkuk, with some 10 percent of Iraq’s oil reserves, has long been contested by Baghdad and Erbil.