Speaker of Parliament Hajim al-Hassani told members a text of the document had been received but said the final wording would have to be worked out within the next three days.
The speaker said he expected remaining differences to be ironed out in the coming days.
He went on to say that there was strong interest in reaching unanimity on the draft "so that the constitution pleases everyone".
"All these groups in the coming three days will try, God willing, to reach an accord," he said.
"The draft constitution has been received and we will work on solving the remaining problems, God willing."
Al-Hassani told reporters that the main outstanding issues were federalism, the formation of federal units, mentioning the Baath Party in the constitution, and the division of powers between the president, the parliament and the cabinet.
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The numerous remaining issues cast doubt on whether the Iraqis would be able to finish the document within a few days since the various groups have widely differing positions on all those points.
Repeated delays are a deep embarrassment for the Bush administration at a time of growing doubts within the United States over the mission in Iraq.
Washington had applied enormous pressure on the Iraqis to meet the original 15 August deadline but parliament instead had to grant a week's extension, which they again failed to meet.
"It is not possible to please everyone," said Humam Hammoudi, Shia chairman of the 71-member committee that struggled for weeks to try to complete the draft.
"But many things have been achieved in this constitution and we hope it will be a real step toward stability."
The Kurds demand federalism to protect their self-rule in three northern provinces.
Sunni Arabs oppose that, fearing Kurds want to declare independence.
The Shia community is divided, with factions supporting federalism wanting to build a Shia region in the south.
The showdown on the constitution came as violence persisted in Iraq.
The US military said two US soldiers from Task Force Liberty were killed on Monday by a roadside bomb during a combat patrol north of Baghdad, and two more soldiers died when their vehicle overturned during a military operation near Tal Afar.
At least 1864 US troops have died since the Iraq war started in 2003, according to Pentagon-based count.
US President George Bush defended the war in Iraq on Monday in the face of growing scepticism, asserting that "a policy of retreat and isolation will not bring us safety".
"The only way to defend to our citizens where we live is to go after the terrorists where they live," Bush said in Salt Lake City in a speech to the national convention of the Veterans of Foreign Wars.