A spokesman said on Saturday that the US-installed Iraqi Governing Council was still meeting and would probably make a statement at 22:00 (19:00 GMT).
"We are not going to have an interim law today," spokesman Jared Young told the AFP news agency.
Mahmud Uthman, a Sunni Kurd on the 25-member council, said on Saturday a decision not to make Islamic law the basis for issues such as divorce and inheritance prompted eight of the council's 13 Shia members to walk out, halting the talks.
Missing the Saturday deadline by a few days will not set back US plans to transfer power on 30 June. But the walkout illustrated the deep divisions in the body running generally along the country's religious and ethnic lines.
It was the first major dispute among council members.
The temporary constitution is an important step leading to the handover of sovereignty from the ruling US-led occupying forces to an Iraqi authority, which is due to take place on 30 June.
The fundamental law is meant to see Iraq through a period of transition and into next year.
Iraq's Shia, long oppressed by Saddam Hussein's regime, are eager to hold power under a new government, worrying the Sunni. Kurds, meanwhile, are pressing to maintain their autonomy in the north.
The talks stalled on resolution 137, which was passed by the council in December abolishing the previous, liberal personal status Law - which governs family law - and allowed each sect in Iraq to apply its own religious law.
Abd al-Aziz al-Hakim, a Shia Muslim who headed the council in December, pushed the decision through, apparently taking advantage of the absence of several council members.
"It was me who recommended that we discuss the issue of resolution 137," said council member Raja Habib al-Khuzaai, a Shia. "The purpose was to affirm women's rights in the interim constitution."
Despite the walkout, she said talks were expected to resume later on Saturday and the interim constitution drawn up.
The resolution sparked widespread protests by women, who feared it would roll back the rights they have.
Foundation of government
The interim constitution is supposed to serve as the foundation of the Iraqi government until a permanent charter can be completed next year. It will serve as the basis of the legal system after the US-led occupation returns sovereignty to the Iraqis on 30 June.
Bremer said he would veto the
proposed sharia legislation
Under the American timetable, the US-picked 25-member council is supposed to finish the document on Saturday for approval by the top US occupation administrator in Iraq, Paul Bremer.
Uthman and other council members said earlier this week that some of the most contentious issues may not be resolved at all in the interim constitution - and could be held over until work starts on a permanent one next year.
Besides the role of Islam, the major differences over the constitution are the extent of Kurdish autonomy and the structure of a collective presidency - whether the body should have three or five members and whether the chairmanship should rotate.
"I prefer a one-person presidency because we already have experience with a rotating presidency in the governing council when each month there is a new different president who has his own agenda," al-Khuzaai said.
Islamic conservatives on the council want the constitution to state that Islam is the main source of legislation and no law should be passed if it is contrary to Islamic values, Uthman said.
"I prefer a one-person presidency because we already have experience with a rotating presidency in the governing council when each month there is a new different president who has his own agenda"
Raja Habib al-Khuzaai,
Shia council member
Bremer has suggested he might veto such language. The US-favoured text would enshrine Islam as one of the sources of law - but not the only one.
The constitution will create a federal system to decentralise power after a long history of Baghdad keeping a strict hold on Iraq's disparate regions.
But council members are sharply divided over the terms of a Kurdish federal region - particularly the status of Kirkuk, an oil-rich region with significant non-Kurdish populations, and the future of Kurdish militias, which the Kurds want to maintain, Uthman said.