The government of Iraqi Kurdistan said on Thursday it was open to talks with Baghdad after central government forces ousted Kurdish troops from disputed territories.
"The cabinet welcomes the initiative of Iraqi prime minister Haider Al Abadi on starting negotiations with the regional government to solve pending issues according to the constitution," it said in a statement.
Mr Al Abadi called for dialogue on Tuesday, saying he considered last month’s referendum, in which Kurds voted overwhelmingly for independence despite Baghdad’s opposition, “a thing of the past”.
The statement was issued after a meeting attended by Iraqi Kurdish prime minister Nechirvan Barzani and deputy prime minister Qubad Talabani.
"Kurdistan demands the help and contribution of the international community in sponsoring this dialogue," the statement said.
Iraqi troops alongside Shiite paramilitary forces pushed into the multi-ethnic city of Kirkuk on Monday as Kurdish fighters gave up their positions.
On Wednesday, the Iraqi military announced its troops had completed the operation to retake not just Kirkuk and its lucrative oil fields, but formerly Kurdish-held areas in Nineveh and Diyala provinces.
An Iraqi court on Thursday issued an arrest warrant for the vice president of the semi-autonomous Kurdish region, Korsat Rasul, after he described Iraqi government forces who entered the disputed city of Kirkuk this week as "occupiers". The warrant adds to mounting tensions between Baghdad and Iraqi Kurdistan following the advance by government troops.
The operation was carried out with minimal casualties as Kurdish forces pulled back, but fears of an outbreak of clashes prompted the UN Security Council to call on Wednesday for all sides to "refrain from the threat and use of force, and to engage in constructive dialogue as a pathway to de-escalation".
The offensive enabled Kurdish peshmerga forces to return to their positions they held in June 2014, before ISIL invaded northern and western Iraq, forcing the Kurds to advance south and take the territory.
About 100,000 Kurds have fled Kirkuk since Iraqi troops entered on Monday, according to the governor of Iraqi Kurdistan's Erbil province.
"About 18,000 families have taken shelter in the cities of Erbil and Sulaimaniya," Nawzad Hadi said on Thursday.
Mr Al Abadi had on Wednesday called upon residents of Kirkuk to remain peaceful, promising that "justice will prevail".
"We warn any group in Kirkuk and the disputed areas of committing any action against citizens under any condition," the prime minister said at his weekly press briefing.
Amid the tensions between Iraqi Kurdistan and Baghdad and among Kurdish political parties, the region's election commission said it had postponed parliamentary and presidential elections due next month.
A new date for the polls, originally scheduled for November 1, would be decided by the Kurdish parliament, the commission said on Wednesday.
The current crisis was precipitated by a Kurdish independence referendum held last month despite objections from most of the international community and Baghdad, which said the poll was against the constitution. The US-led coalition against ISIL said it would jeopardise the fight against the extremist group, in which Kurdish forces have played a key role.
In an article for The New York Times on Wednesday, Mr Al Abadi wrote: "I had hoped that just as we united to defeat our enemy [ISIL], we would unite to recover and rebuild. Many Iraqis were therefore shocked by the unilateral action of some elements of the Kurdish leadership — key architects of the 2005 Iraq Constitution, which enshrines and protects Iraq's federalism — in holding an illegal referendum last month."
Describing the referendum as "an act of deliberate division, Mr Al Abadi called on the Kurdish Regional Government to acknowledge the authority of the Iraqi constitution and to enter dialogue with Baghdad.
The Kurdish region has also come under pressure from neighbouring countries over the independence vote. Turkish president Recep Tayyip Erdogan said his country may shut its border with northern Iraq "at any moment" after earlier closing its air space to the region, Hurriyet newspaper reported on Thursday.
"We have completely closed our air space to the regional government in northern Iraq," Mr Erdogan told reporters aboard his plane returning from a trip to Poland.
"Talks are continuing on what will be done regarding the land border. We have not shut the border gates yet but this could happen too at any moment."