Hajim al-Hassani, a Sunni, said late on Friday no accord had yet been clinched and a final decision would only be clear on Sunday.
Al-Hassani said that negotiators from the Shia majority had proposed a number of amendments to an existing draft to meet Sunni demands.
Sunni leaders had yet to give a definite response, he said, but the amendments did deal with those issues which were troubling the Sunnis.
If there were no agreement by Sunday there would definitely be no further discussion, al-Hassani said, and a final draft based on Shia and Kurdish proposals would be put to October's referendum without the support of the Sunni delegates.
"There is a deal in principle," he said. "Today we had a response from the Shia. Tomorrow the Sunnis are going to meet and we expect a response on Sunday," he said.
"Definitely on Sunday ... we will either announce an agreement but if their (the Sunnis') response is negative we will go to the referendum anyway."
Speaker al-Hassani says a clear
decision would be taken by Sunday
The compromise from the Shia concerned federalism, among other things.
Earlier, a spokesman for Deputy Prime Minister Ahmad Chalabi, a secular Shia, said there was a deal and said that the Shia and Kurdish government parties had agreed to leave the mechanisms for setting up federal regions to be decided by parliament after a December election.
Legislation on excluding former members of Saddam Hussein's banned Baath Party from public life would also be left in the hands of a new parliament, he said, addressing Sunni concerns.
Earlier during the day, Shia negotiators confirmed they had offered their final compromise proposal to Sunni Arabs to try to break the impasse over the new constitution.
The Shia are awaiting a response from the Sunnis, key negotiator Abbas al-Bayati said.
Secretary-General of the Islamic Party in Iraq Tariq al-Hashemi told Aljazeera that the Sunnis had asked for 24 hours to respond to the new proposals presented to them by the Shia.
Al-Hashemi said the fresh proposals still seemed below the minimal requirements of the Sunnis.
"There are also a number of unresolved issues that are still pending including identity of Iraq, the state revenues, the issue of citizenship in addition to powers and authorities granted to regions," he said.
Shia negotiator al-Bayati said the new proposals were on the pivotal issues of federalism and efforts to remove former members of Saddam's Sunni-dominated Baath Party from public life, adding "we cannot offer more than that".
"Today we had a response from the Shia. Tomorrow the Sunnis are going to meet and we expect a response on Sunday"
speaker of Iraqi parliament
Al-Bayati said the Shia had proposed that the parliament expected to be elected in December be given the right to issue a law on the mechanism of implementing federalism. He gave no further details.
On the Baath Party, he said it would be up to the next parliament to set a timetable for the work of the Supreme National Commission for de-Baathification.
Al-Bayati said United States President George Bush telephoned Shia leader Abdul-Aziz al-Hakim on Thursday and urged a "consensus" on the draft constitution.
"Today we reached the final limit beyond which we can't move any further," said Jawad Maliki, the number two in the Shia Dawa Party of Prime Minister Ibrahim al-Jaafari.
"Our final proposal stipulates removing all obstacles to federalism and putting every obstacle in the path of the resurrection of the Baath Party and continuing to prosecute its leaders," he said.
"Sunnis want to revive the Baath Party and stop the process of de-Baathification, and they want to obstruct federalism," he said.
"This we cannot accept."
The Sunnis insist that the issue of dividing Iraq into federated regions be deferred until after the new parliament due to be elected in December.
Many Sunnis boycotted the 30 January election for the current parliament, which is dominated by the Shia and Kurds.
If voters reject the charter,
parliament will be dissolved
Earlier, Sadoun Zubaydi, a Sunni member of the drafting committee, said the Sunnis would have to see the fine points of the Shia proposal first.
If the proposal does not make concessions on the principle of federalism but only the mechanism, this would not meet Sunni demands.
"Our position is that both the principle and mechanism should be deferred," Zubaydi said.
"Our policy is decentralisation, but not political federalism with borders, division of resources, etc. That is separatism, not federalism."
Al-Bayati and fellow Shia negotiator Ali al-Adeeb, a Shia member of the committee drafting the charter said Bush telephoned al-Hakim after negotiations were deadlocked and it appeared the draft submitted to parliament last Monday would go to the voters in the 15 October referendum as is.
Al-Adeeb said US ambassador Zalmay Khalilzad had also appealed to Iraq's powerful Shia clergy, including Grand Ayat Allah Ali al-Sistani, to help resolve the
Meanwhile, on Friday, about 5000 people, some carrying Saddam's picture, rallied in Baquba city to protest the draft constitution.
The rally was organised by the Iraqi National Dialogue Council, a Sunni group whose spokesman is a constitution negotiator.
Sunni Arabs fear that federalism will lead to the breakup of the country.
Kurds oppose limiting the size
of their self-ruled area
Zubaydi said the Sunni delegation had proposed granting the Kurdish north -consisting of three provinces - full federal status, with decentralised local government for the remaining 15 provinces.
The Sunnis want federalism limited to three provinces, while the current draft sets no limit on the number which could join a federal region.
The Kurds oppose measures which would limit the size of their self-ruled area because they want to incorporate oil-rich Kirkuk - which contains substantial non-Kurdish populations.
The bitter negotiations, rather than serving to bring the country's disparate ethnic, cultural and religious groups closer together, appear instead to be pushing them further apart.
Although the constitution requires only a simple majority in the referendum, if two-thirds of the voters in any three of Iraq's 18 provinces vote against it, the charter will be defeated.
If voters reject it, parliament will be dissolved and elections held by 15 December to form a new one. The new parliament then starts drafting a new constitution.