A KRG official said the deadline for Peshmerga fighters to leave the city of Kirkuk stands until Sunday night.
Baghdad has set a pre-dawn Sunday deadline for Kurdish Regional Government forces (Peshmerga) to abandon positions in the disputed oil province of Kirkuk they took during the fightback against Daesh, a senior KRG official said.
The reported ultimatum comes as thousands of Iraqi troops and allied militia are locked in an armed standoff with KRG Peshmerga fighters near ethnically divided but historically Kurdish-majority Kirkuk.
Tensions have soared between the erstwhile allies in the war against Daesh since a Kurdish vote for independence last month, drawing urgent appeals for calm from the US-led coalition supporting the campaign.
"The deadline set for the Peshmerga to return to their pre-June 6, 2014 positions will expire during the night," the KRG official said asking not to be identified.
Asked at what time, he said 2am on Sunday (2300 GMT Saturday).
The official's comments came as Iraqi President Fuad Masum, who is himself a Kurd, was holding urgent talks with KRG leaders in the city of Sulaimaniyah in the south of the semi-autonomous Kurdish region.
No statements have emerged from the meetings.
On Friday, Iraqi troops took over formerly Kurdish-held positions in the south of Kirkuk province, including in the Turkmen town of Taza Khurmatu.
In June 2014, Daesh militants swept through vast areas north and west of Baghdad, prompting many Iraqi army units to disintegrate and KRG forces to step in.
They did so primarily in Kurdish-majority areas they had long sought to incorporate in their three-province autonomous region in the north against the strong opposition of Baghdad.
The Kurds currently control the city of Kirkuk and three major oil fields in the province which account for a significant share of the regional government's oil revenues.
US Defence Secretary Jim Mattis said on Friday that Washington was working to reduce tensions between Iraqi federal and KRG forces, urging them to remain focused on the war against Daesh.
"We are trying to tone everything down and to figure out how we go forward without losing sight of the enemy, and at the same time recognising that we have got to find a way to move forward," he told reporters.
"Everybody stay focused on defeating ISIS [Daesh]. We can't turn on each other right now. We don't want to go to a shooting situation," he added.