But when the Security Council voted unanimously to adopt resolution 1546 on 8 June, any mention of the interim agreement -- known as the Transitional Administrative Law -- was conspicuously absent.
Iraqi Prime Minister Iyad Allawi has since said his government will adhere to the interim constitution until elections are held next year.
But his remarks have failed to appease the Kurds, who are worried the Transitional Administrative Law will be sidelined -- and their aim of autonomy along with it.
Speaking yesterday in New York, UN envoy Lakhdar Brahimi expressed confidence that Iraqi Kurds would continue to participate in the country's political process.
"I think the leaders of Iraqi Kurdistan understand and are fully aware what the geostrategic realities of the region are. And I think that talking to [Kurdistan Democratic Party head] Massoud Barzani and talking to [Patriotic Union of Kurdistan head] Jalal Talabani and to their people, one has a strong impression that they want to contribute very effectively to the building of new Iraq in which their region will be a full partner," Brahimi said.
The debate over the interim constitution reflects the concerns of two ethnic groups who are trying to redress their past sufferings -- the minority Kurds, and the majority Shi'a Muslims, who held virtually no political power under Saddam Hussein.
The interim constitution currently blocks the possibility of majority rule advocated by the Shi'a.
That is because it states the permanent constitution will pass on a popular majority vote -- unless it is rejected by two-thirds of the voters in three of Iraq's 18 provinces. Iraq has three provinces with a Kurdish majority.
Brahimi characterized the dispute as two sides talking about two different things. The Shi'a are defending the rights of the majority, and arguing against any faction holding a blanket veto. The Kurds, meanwhile, are focused on guaranteeing the rights of minorities -- a mindset that has hardened through decades of suppression and broken promises.
"[Kurds] want to be absolutely certain now, in the Iraq to which they are returning, that they will be -- as they put it -- not second-class citizens but full partners in the federation that is going to be constructed between themselves and the other Iraqis," Brahimi said.
Brahimi said neither side should be punished for their stance on the issue, and conceded that resolving the problem will be a challenge. He expressed faith that both the Shi'a and the Kurds will act responsibly to find a workable solution.
"I think the Kurds have a case in making absolutely certain that -- the way they put it is, 'We have been cheated very, very often in the past and we don't want to be cheated again.' There is a real, real problem here. It's not that the Shi'a are being unreasonable or that the Kurds are being greedy," Brahimi said.
Some UN diplomats, however, have expressed doubts the problem will be resolved quickly or easily, saying they hope the debate will not develop "into anything ugly."
Despite the disappointment of the Kurds over the wording of the new UN resolution, other Iraqis say the Security Council agreement gives a boost to the 30 June transfer of sovereignty to the Iraqis.
Speaking on 8 June at the New York-based Council on Foreign Relations, Iraqi Foreign Minister Hoshyar Zebari said the UN endorsement will grant greater legitimacy to Iraq's new interim government.
"There is also the question of how legitimate this new interim government is, since we haven't had the chance to have elections or to have an elected representative government," Zebari said. "So, with the involvement of the United Nations, with its providing some international legitimacy to the new interim government, I think it will be more acceptable to the people of Iraq, to the region. Especially, it will not be seen as purely an American-led operation."