The United Nations has criticised changes to Iraq's electoral law that make it harder for Iraqis to reject the draft constitution.
They believed many registered voters may not show up at the polls because of violence.
"We have expressed our position to the national assembly and to the leadership of the government," said Jose Aranaz, a legal adviser to the UN electoral team in Iraq, in an interview with Reuters news agency.
Mr Aranaz said parliament's decision was unacceptable and would not meet international standards.
"Hopefully by tomorrow the situation will be clarified," he said.
Many Sunni Arabs oppose the draft constitution on the grounds that its federal provisions could lead to the break-up of Iraq.
They are the majority in three Iraqi provinces, but largely boycotted the general election in January this year.
The drafting of a constitution and a national vote on it, were meant to draw Sunni Iraqis into the political process, thereby reducing support for the mainly Sunni backed insurgency.
On Monday Saleh al-Mutlaq, of the Sunni group Iraqi National Dialogue, called the change the voting law a "clear forgery".
"They want this constitution to pass despite the will of the people," he added.
The interim constitution drawn up under US administrator Paul Bremer in 2003 says the following about the issue: "The general referendum will be successful and the draft constitution ratified if a majority of the voters in Iraq approve and if two-thirds of the voters in three or more governorates do not reject it."
But on Sunday, MPs said a No vote from two-thirds of "registered" voters was needed for a veto.
The new interpretation keeps the clause stipulating that only half of actual voters are needed for the text to be adopted.
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