The offer came as world powers scrambled to avert any further escalation of the conflict between the key allies in the fight against the Islamic State group that has seen more than 30 combatants killed.
Washington, Moscow and the United Nations have all pressed Iraqi Kurdish leader Massud Barzani to open talks with Baghdad on a way out of the crisis sparked by the fateful September 25 vote that he called.
It also called for "an immediate ceasefire and cessation of military operations in Kurdistan".
Since early last week, Iraqi federal troops and allied militia have retaken virtually all of the territory held by the Kurds outside their longstanding three-province autonomous region in the north.
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In most areas the Kurds withdrew without a fight, although in the Little Zab valley close to their regional capital Arbil there was fighting and in all at least 31 combatants were killed.
The loss of so much territory, including the major city of Kirkuk and lucrative oil fields, dealt a huge blow to Kurdish dreams of economic self-sufficiency and eventual independence.
Barzani's longtime political rival, the Patriotic Union of Kurdistan, had opposed the independence vote and backed a UN plan for negotiations on wider Kurdish autonomy.
The Iraqi constitution adopted during the US-led occupation of 2003-11 provides for plebiscites in the disputed areas on their possibile incorporation in the autonomous Kurdish region.
Washington has made clear that while it will not take sides in the conflict between its Iraq allies, it does not regard Baghdad's reoccupation of the disputed areas as a fait accompli.
The United Nations said on Tuesday that it stands ready to broker talks.
UN envoy Jan Kubis "expressed confidence that despite the recent tensions, Iraq will be able to ride this crisis".
"Both sides publicly expressed their willingness to engage in dialogue and negotiations on the basis of the Constitution. The UN is ready to assist, if requested," he said.
"We are confident that the Government of Iraq and the Kurdistan Regional Government, just like they banded together to defeat Daesh (the Islamic State group), can work hand in hand to overcome their differences through dialogue and away from confrontation to resolve all outstanding issues in a manner that is consistent with the constitution."