Iraqi political leaders have agreed amendments to the draft constitution as they try to reach consensus on the document, a government spokesman said.
Sunni Arabs have taken to the streets to oppose the draft
Laith Kubba said amendments had now been made to three disputed articles. He expected the draft to be completed by the end of Thursday.
The Shia, Kurdish and Sunni negotiators had been given three more days from Monday to secure consensus.
But no deal was apparently reached and talks are to set to continue on Friday.
"This is a good sign and we hope we will reach a result tomorrow night," parliament speaker Hajim al- Hassani told Reuters news agency as the Thursday deadline - the third so far - passed.
15 August deadline extended twice
National referendum on constitution by mid-October
Full government elections by mid-December
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The interim government has acknowledged that differences will remain.
The outstanding issues included provisions on federalism, which is opposed by the Sunni Arabs, who fear the break-up of Iraq.
Adding to the tensions surrounding the constitution, on Wednesday seven people died in clashes between rival Shia in several Iraqi cities.
On Thursday, police reported the discovery of the bodies of 36 men dumped in a shallow river near the eastern Iraqi town of Kut.
They were partially clothed, had been handcuffed and all had been shot in the head in an execution style.
Shia and Kurdish leaders have reached agreement on the entire text of the constitution - and could approve the document in parliament without Sunni backing.
But the insurgency that still plagues Iraq has its roots in the Sunni heartlands and the constitution is supposed to be part of the process of winning the Sunni community round, BBC Baghdad correspondent Mike Wooldridge says.
The original deadline last week was postponed twice - giving negotiators 10 extra days to reach a deal.
The outstanding issues from the Shia-Kurdish draft submitted on Monday included:
- federalism, and the way to form [federal] regions
- the terminology used in eradicating the influence of the former Baath regime - whether to use the term Baath party or Saddam's Baath
- structuring of authority between the presidency, parliament and the government.
A copy of the draft constitution circulated earlier in the week says that Iraq's future lies in a democratic, federal, republican system - free of sectarian or racial discrimination and with a fair distribution of wealth.
Sunnis have expressed concerns that allowing for federalism may lead to the creation of an autonomous Shia area in southern Iraq - like the Kurdish north but under Iran's influence.
The Sunnis fear greater autonomy for the Kurdish north and Shia south could compromise their share of revenues from those oil-rich regions.
The US has announced it is sending another 1,500 troops to Iraq to bolster security before a referendum on the constitution, due in October.
It seems that the battleground will now shift to the referendum, our Baghdad correspondent says.