Shia officials in Iraq say they have agreed with the Kurds the draft text for a constitution - and are presenting it to parliament for approval.
The sharing of Iraq's oil revenues is still under discussion
But minutes ahead of the deadline for an agreement, Sunni politicians said there was no consensus.
The original deadline last week was shifted to midnight on Monday (2000 GMT) when no agreement was reached.
MPs have gathered in the chamber to receive the text but it is not clear what decision they will make.
Shia and Kurdish political groups have enough of a majority in parliament to push through a draft constitution without the support of Sunni members of parliament.
Correspondents say this would be a politically damaging move, possibly further alienating Sunni Iraqis from the political process.
US officials say a delay risks playing into the hands of the insurgents, who killed 10 people in Baghdad on Monday.
Eight policemen were among those killed as their mini-van was riddled with bullets north of the capital.
Shia, Sunni and Kurdish teams have had difficulties agreeing on key issues including federalism, oil and the role of Islam.
"Thank God we have finished all the details related to the agreement," Shia negotiator Jawad Maliki told reporters.
He acknowledged differences with Sunni Arabs over the key issue federalism - which they oppose for all but Iraq's northern Kurdish area.
The Sunnis oppose greater autonomy for the Kurdish north and Shia south, fearing its share of revenues from those oil-rich regions could eventually be compromised.
And Sunni negotiator Saleh Mutlaq said "major points of disagreement" remained and the plan to submit the text to parliament was unlawful.
"There is still no agreement and if they want to hand the draft today they will be violating the law," Mr Mutlaq told the Associated Press news agency.
One prominent Kurdish negotiator, Mahmoud Othman, said earlier the Shia insistence on submitting the draft had created a lot of bad feeling.
He said it was important to have the Sunnis on board.
The prime minister's spokesman has said the government may ask for another one-week extension or "the national assembly would be dissolved" paving the way for fresh elections.
Correspondents say there appears to be little appetite for new elections, so an extension appears the more likely outcome if the deadline is not met for the second time.
The United States has led the way in urging the completion of the constitution, seeing it as a step towards stabilising Iraq.
The BBC's Mike Wooldridge in Baghdad says Sunni politicians complain of being sidelined and have urged the international community to prevent the pushing through of a constitution lacking consensus.
He says the most optimistic participants believe a final text at this stage would still leave some details unresolved.
Officials say the communities have edged closer on some issues, but not close enough to come up with a draft form of words for the constitution.
A draft constitution agreed by the committee would be put to a referendum due in October.
If it was approved, fresh elections would follow to elect a fully-mandated parliament under its terms, probably in December.