The National Security Council said it viewed as a "dangerous escalation" and a "declaration of war" the presence of "fighters not belonging to the regular security forces in Kirkuk", including fighters from Turkey's outlawed Kurdistan Workers' Party (PKK).
"It is impossible to remain silent" faced with "a declaration of war towards Iraqis and government forces", the council headed by Iraqi Prime Minister Haider al-Abadi said in a statement.
The statement came just hours before the expiry of a deadline for Kurdish peshmerga fighters to withdraw from areas they took in Kirkuk in 2014 during the fightback against the Islamic State jihadist group.
Crisis talks today made little headway in resolving an armed standoff between Kurdish and Iraqi forces in the province.
Tensions have soared between the central government and Iraqi Kurds since they overwhelmingly voted for independence in a September 25 referendum, whose results Baghdad has demanded be nullified.