But Mahmud Othman, a Kurdish member of the constitution committee, told AFP:
"If we see that our right to self-determination becomes the only obstacle in finalising the constitution, our parliament will be flexible and not be an obstacle."
The conciliatory announcement appears aimed at helping Kurdish, Sunni and Shiite negotiators finally forge an agreement on a new draft constitution on time after weeks of exhausting talks and a previous missed deadline.
But in another possible hitch to the already marathon process, Iraqi leaders were becoming engulfed in a debate over whether to make Islam "the" main source of legislation or just "a" main source.
Sources close to negotiations said the debate was triggered after the United States surprisingly dropped its opposition to enshrining Islam as Iraq's main source of legislation.
They said the US move was aimed at securing agreement on the text of a new constitution by the Monday deadline.
Washington is determined to see the target date met after the first deadline was missed last Monday, fearing that any loss of momentum in the political process will play into the hands of Sunni Arab insurgents.
"Last night's talks had a surprise element -- the Americans appeared to give in to the demand from various Islamic groups that Islam be the main source of legislation," one source told AFP, adding that US ambassador Zalmay Khalilzad was present at the negotiations.
But Othman said the Kurdish leaders will oppose any move to make Islam the main source of legislation.
"We will oppose this as much as we can," he stressed. "This is politics... we believe that the constitution should not impose any ideology on the people and help develop a free society."
The role of Islam in lawmaking has proved a heavily divisive issue among negotiators, with leaders of Iraq's Shiite majority insisting religion be considered the main legal foundation, and that clerics be given political roles.
Kurds and other secularist groups oppose the Shiite demand, arguing that it would harm women's rights and Iraq's secular tradition.
One Western diplomat with high-level involvement in the negotiations played down the significance of a strong role for Islam in the new constitution.
"There's not a country in the region which does not have Islam as a main source of legislation," the diplomat said on condition of anonymity. "(The issue has) no real jurisprudential significance, it's more symbolic."
Drafting committee members said more talks were scheduled for Saturday after Friday evening's session made little progress on key issues, which also include federalism and a mechanism for distributing the state's huge oil revenues.
The Shiite and Kurds have a comfortable majority in parliament and observers have speculated that they may forge a compromise over the heads of Sunni negotiators in order to meet Monday's deadline.
But a Sunni committee member warned Friday that such a deal would likely be rejected by voters from the disenchanted former elite in a referendum scheduled for October.
"The people of Iraq will defeat a federal constitution in the October referendum," Saleh al-Motlag said.
"We are against the principle of federalism because we want the country to be centrally governed."
Under the terms of interim legislation, the constitution fails if two-thirds of the voters in any three of Iraq's 18 provinces reject the text in the referendum.
The Sunnis form a majority in Al-Anbar, Ninevah and Salaheddin provinces, and they have a strong presence in Tamim.
Meanwhile, Ashraf Qazi, special Iraq representative of UN secretary general Kofi Annan, said he "deeply regrets" the decision of an Iraqi government "in the process of transition" to reinstate the death penalty.
The Iraqi government has announced that three members of the Al-Qaeda affiliate group Ansar al-Sunna will be sentenced to death for kidnapping policemen and raping Iraqi women.
Violence persisted on Saturday with rebels killing ten people across Iraq, including three Iraqi soldiers who died in a grenade attack in the former rebel enclave of Fallujah.