That document, called the Transitional Administrative Law, recognizes the continued right of the country's Kurds to autonomy. But it postpones decisions on the region's final status.
The autonomy question appeared to receive a setback when the UN failed to mention the interim constitution in its latest resolution on Iraq sovereignty.
The omission sparked an uproar among Iraqi Kurdish parties that has yet to be resolved, despite promises by interim Iraqi Prime Minister Iyad Allawi to respect the Transitional Administrative Law.
Omar Aziz Kader, a spokesman for the Patriotic Union of Kurdistan (PUK), told RFE/RL his party is worried that Allawi is giving empty promises.
"[We've heard] only words, we haven't got anything written about that matter. We hoped [before] that the United Nations would mention at least something about the Kurdish people [in its resolution,] but unfortunately there is nothing," Kader said. "We just say that what has happened are only verbal promises, but we don't plan to take any actions against the new Iraq, which is building democracy."
Kader said the PUK is still trying to resolve the issue of autonomy peacefully, through negotiations, and that the party has no intention of walking away from the political process.
There is a suggestion, however, that Kurds -- and the 75,000 peshmerga fighters they employ -- are prepared to go beyond negotiations to secure their goal of autonomy.
"There is an administrative law," said Faraj al-Haydari, an official with the Kurdistan Democratic Party (KDP). "This law should be implemented. If it is implemented, we will have achieved what we want. If it is not implemented, if it is canceled, we will take different measures than we are taking now."
The Kurds face a powerful challenger in Iraq's Shi'a Muslim majority, including leaders like Grand Ayatollah Ali al-Sistani, who strongly opposes the Kurdish rights guaranteed in the interim constitution -- including veto power over political decisions.
Kurdish leaders also express disappointment in the United States. Kader said many Kurds say they expected support from Washington in return for their help in ousting Saddam Hussein, but instead have received nothing.
"Up to now [we have received] nothing [from the United States], but we hope. We hope they will understand our point [of view]," Kader said. "We hope they will understand our position in this area. We are a nation that has always liked peace, liked something good for the whole world -- not just for Iraqi people."
However, not everybody in Iraq agrees. The potential borders of a Kurdish autonomous region have yet to be settled. The Kurds continue to demand oil-rich Kirkuk, which holds some 30 percent of Iraq's oil reserves. Though the Kurds make up a substantial part of Kirkuk's residents, the Arabs and Turkomans also living in Kirkuk do not accept their territorial claim.
Kader said the transfer of power on 30 June should help to resolve the problem -- and hopefully to the benefit of Kurdish people.
"The Kirkuk question is still on the table. We are still talking about it. The allied forces -- that is, the Americans and their allies inside Iraq -- did nothing for us, for the Kurdish people, and they ignored us totally," Kader said. "But we hope that the new government is going to [act on the behalf of] the Kurdish people in Kirkuk."
He said the Kurds who were expelled from Kurdistan during Saddam Hussein's Arabization campaign should be allowed to go back and that a referendum should be held on the future of Kirkuk.
But this suggestion will be difficult to swallow, not only for Shi'a politicians, but also for Iraqi Sunnis and Turkomans. Iraq's neighbors have a stake in the issue as well -- primarily Turkey, which continues to grapple with its own issues of Kurdish autonomy.