A deadline allegedly set by Iraq's central government for Kurdish fighters to withdraw from key sites in the disputed city of Kirkuk has passed.
Kurdish security officials said the deadline had been set for early on Sunday but Iraqi authorities denied it.
Some reports now suggest the deadline has been extended by 24 hours.
Both sides have sent troops to Kirkuk and brief clashes have already erupted between Kurds and Shia militia backing the government.
Peshmerga fighters say they are preparing to defend positions in the city against possible attack by Iraqi forces.
Tensions have been on the rise since Kurds held a referendum on independence last month, which Iraq called illegal.
The Iraqi parliament asked Prime Minister Haider al-Abadi to send troops to Kirkuk and other disputed areas after the official referendum results - which overwhelmingly backed independence - were proclaimed.
The referendum was held in three autonomous provinces of Iraqi Kurdistan, but also in nearby Kurdish-held areas including Kirkuk.
The province, which bears the same name as the city, is thought to have a Kurdish majority, but Kirkuk has large Arab and Turkmen populations.
On Saturday, there was a brief outbreak of fighting near Kirkuk, with each side blaming the other, reports the BBC's Orla Guerin in Iraq.
Mr Abadi said last week he would accept disputed areas being governed by a "joint administration" and that he did not want an armed confrontation.
On Thursday, the prime minister and the Iraqi military reiterated that they had no plans for a military operation in Kirkuk and were focused on recapturing the last IS foothold in Iraq near the border with Syria.
But since then there has been a major build up of Iraqi forces around the city and Kurdish officials say the Peshmerga have been ordered to defend their positions "at any cost".
The 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.