Parliament adjourned after voting to extend the deadline to 22 August, acting on a request from Kurdish leaders for more time after politicians failed to meet a Monday midnight deadline for agreement on the charter.
Shia, Sunni and Kurdish framers of the constitution had reached a tentative deal late on Monday, resolving issues ranging from oil revenues to the country's name but putting off decisions on the most contentious questions, including federalism, women's rights, the role of Islam and possible Kurdish autonomy.
An initial agreement to share the oil revenues has been agreed to, but the mechanism to distribute it remains to be formulated.
Efforts to meet the 15 August deadline showed how determined Iraqis are to maintain political momentum under intense US pressure, but their failure to compromise was a clear sign that their sharp political divisions are far from over.
"We should not be hasty regarding the issues and the constitution should not be born crippled"
Iraqi President Jalal Talabani
"We should not be hasty regarding the issues and the constitution should not be born crippled," President Jalal Talabani, a Kurd, said after the vote.
"We are keen to have an early constitution, but the constitution should be completed in all of its items in a proper manner that appeals to all components of the Iraqi people so that the whole people interact with the whole constitution."
It was unclear if negotiators would reopen issues already resolved or focus only on those yet undecided.
Meeting the Monday deadline would have been a victory for US President George Bush's administration, which had made clear in recent weeks that it was pushing for a constitution by then, even if some issues were left undecided.
In a sign of Washington's close involvement in the process, the American ambassador to Iraq, Zalmay Khalilzad, was in the hall as parliament gathered.
"There have been substantial agreements, but they need a week to finalise it," Khalilzad said.
Under the country's interim law, a constitution was due to be drafted by 15 August and then put to a referendum in mid-October ahead of new elections in December.