Lt. Gen Wasta Rasul said Kurdish forces known as the peshmerga evacuated positions southwest of city, while an officer in the Iraqi Army's 9th Armored Division said federal forces had moved into positions left by the Kurdish forces in the same area, near the village of Bashir.
Kurdish officials say they have been alarmed by military movements outside Kirkuk.
On Wednesday, Iraq issued the warrants against Hendreen Mohammed, the chairman of the KRG's referendum commission, and two aides for violating an Iraqi court ruling that renders the independence vote "invalid" despite a vast majority of Kurds voting in favor of independence, adds the news agency.
Iraq's government has taken a series of measures to isolate the region since the Kurds' Sept. 25 referendum on independence, including banning worldwide flights from going there and pushing for a halt to its crude oil sales.
One of them, Khasro Abdallah, vowed "to defend Kirkuk to the death".
The Kirkuk province is not officially included in Iraqi Kurdistan, but it is in fact partially controlled by Kurdish Peshmerga detachments.
The Peshmerga took control of Kirkuk when Iraqi defenses crumbled in the face of the advancing Islamic State group in 2014.
On Sept. 25, Iraqis in KRG-held areas - and in several areas disputed between Baghdad and Erbil, including Kirkuk - voted on whether or not to declare independence from Iraq.
Since then, the Iraqi army and the peshmerga have been key allies of the US-led coalition in its fight against the Islamic State group.
Rassoul Omar, another peshmerga general, said his fighters were mobilising south of Kirkuk.
Sources in Kirkuk also confirmed to Al Jazeera the movement of Iraqi forces on two fronts in Kirkuk, in the south and west of the city.
Some troops were busy daubing paint on cement blocks which had been stamped with the Kurdish flags.
In 2014 "the peshmerga prevented IS from attacking the oil infrastructure. and protected the residents of Kirkuk", said commander Sheikh Mustafa.
"Baghdad would do better to find another way to resolve the problems than send troops", he said. Earlier Baghdad dismissed the governor of Kirkuk and chose to deploy troops to the province.
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