Iraqi forces are advancing towards Kurdish-held sites in Kirkuk province.
They intend to take control of oil fields and an airbase in the disputed region, Kurdish security officials say.
Tensions between the two sides over the future of Iraqi Kurdistan have been high since Iraqi Kurds voted for independence in September.
Crisis talks on Sunday failed to resolve the standoff as Kurdish leaders refused Iraqi government demands to reject the referendum result.
The Iraqi troops were advancing alongside government-backed Shia militias south of Kirkuk city, Kurdish officials reported.
The Iraqi government says its aim is to “secure bases” and “federal installations” but “co-operate” with Kurdish Peshmerga fighters.
Hemin Hawrami, an aide to Kurdish leader Massoud Barzani, tweeted that Kurdish Peshmerga fighters were “in full control” of the airbase.
He earlier said Kurdish leaders rejected the “military option” but were “ready to defend” the city against outside forces.
Baghdad has accused the Kurdistan administration of deploying outside fighters to Kirkuk, including from the Turkey-based Kurdistan Workers’ Party (PKK), which it said was akin to a declaration of war.
The Iraqi Kurds deny this.
On Saturday, there was a brief outbreak of fighting near Kirkuk, with each side blaming the other.
Oil-rich Kirkuk province is claimed by both the Kurds and Baghdad, though the two sides were recently united in the fight against the Islamic State (IS) jihadist group.
Kurdish Peshmerga forces took control of much of the province in 2014, when IS militants swept across northern Iraq and the army collapsed.