Clashes were reported between Iraqi forces and Iraqi Kurdish fighters after Baghdad sent troops towards Kurdish-held sites in Kirkuk province.
State TV report that Iraqi forces have taken control of some areas, including oil fields, “without fighting”, but Kurdish officials deny this.
An exchange of artillery fire is said to have occurred south of Kirkuk city. The US government says it is very concerned and urged dialogue “as the best option to defuse tensions”.
Tensions between the two sides over the future of Iraqi Kurdistan have been high since Iraqi Kurds voted for independence in a September referendum. Kirkuk is not part of the autonomous Iraqi Kurdistan region.
Baghdad wants to retake bases and oil fields taken by Kurdish Peshmerga fighters in 2014 when militants from so-called Islamic State (IS) swept across northern Iraq and the army collapsed.
Crisis talks on Sunday failed to resolve the standoff as Kurdish leaders refused Iraqi government demands to reject the referendum result.