"They have decided that it would be inappropriate to hold a signing ceremony before the end of Ashura," a senior US-led occupation official said on Sunday.
The official was referring to the religious holiday marking the death of prophet's Muhammad grandson al-Husayn in the 7th century.
"There was real reluctance in the message it would send to the Iraqi community if they held a big signing ceremony before the end of Ashura, that was what they were saying last night but I do not know if that might change."
The official said there were no guarantees, but he remained optimistic an agreement would be reached on Sunday, before a signing. "I think we will be able to finish the document today," he told a group of reporters.
Members of the US-appointed Governing Council have been working day and night to finalise the temporary constitution, apparently aimed at seeing Iraq through a period of transition before elections and into next year.
But strong divisions have surfaced, mainly over the role of
Islam and women as well as about Kurdish federation demands, and they have exposed in an unprecedented way the religious and ethnic divisions within the council.
The temporary constitution is an important step in clearing the way for a 30 June transfer of sovereignty from the occupying coalition forces to an Iraqi interim authority.
Council members met almost until dawn on Sunday after missing their midnight deadline, working in groups on almost 60 points that still had to be resolved. The council was due to meet again in full at around 2:00 pm (11:00 GMT).