Iraq's US envoy has met senior negotiators of the new constitution in an attempt to broker a deal on the deadlocked draft proposals.
Hassani said the revised text will be put to parliament on Sunday
Ambassador Zalmay Khalilzad also appealed to the powerful Shia clergy, including Grand Ayatollah Ali al-Sistani, to help break the deadlock.
A revised constitution will be put to MPs on Sunday after Shia and Kurd factions agreed on several amendments.
But Sunni Arab politicians rejected the draft, describing it as dangerous.
Mr Khalilzad held talks with parliament speaker, Hajim al-Hassani, and representatives from the main parliamentary factions, in an attempt to find a compromise on a wording in the constitution acceptable to the Sunnis.
The chief Sunni representative, Saleh al-Mutlaq, said negotiators had done as much as they could and it was now up to the Iraqi people to decide on the constitution in a referendum in October.
But the BBC's Jon Brain in Baghdad says prospects of agreement thus look remote, despite Mr Hassani's upbeat assessment.
'Beginning of division'
Meanwhile, the US military has announced the release of 1,000 inmates from the notorious Abu Ghraib prison.
US officials have refused to say whether the decision to let the prisoners go is related to the talks over the constitution.
However our correspondent says that the release, which follows Sunni appeals, can only be seen as a positive move in the current climate.
Mr al-Mutlaq told al-Jazeera television that compromises offered by the Shias, following proposals submitted by the Sunnis, were "still far from what we need".
15 August deadline extended twice
National referendum on constitution by mid-October
Full government elections by mid-December
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"The Iraqi people have to give their word now and reject the constitution because this constitution is the beginning of the division of the country and the beginning of creating disturbance in the country," he said.
The outstanding issues from the Shia-Kurdish draft submitted last Monday included:
- federalism, and the way to form semi-autonomous 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.
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 original deadline last week was postponed twice - giving negotiators 10 extra days to reach a deal.
Iraq's Shias are expected to back the draft constitution
Shias and Kurds could approve the document in parliament without Sunni backing.
But the insurgency that still plagues Iraq has its roots in the Sunni heartlands. It was hoped the constitution would help win the support of the community for a new Baghdad government.
It has emerged that US President George W Bush phoned a Shia leader earlier this week urging him to be more flexible with regard to Sunni demands.
Meanwhile, thousands of Sunni Muslims demonstrated in the Iraqi city of Baquba on Friday to protest against the constitution being debated in Baghdad.