A Shia negotiator said on Monday that a draft constitution would be presented shortly to parliament, but a key Sunni Arab delegate said talks of a deal were premature and he doubted an agreement was possible by the midnight deadline.
"An agreement between the Shia and the Kurds (the two main parliamentary blocs) has been reached...God willing, the draft will be presented in the parliament today," Shia negotiator Jawad al-Maliki said.
"There is still one point left and the meeting now is about it: It is the Sunni Arab brothers and their stance towards federalism."
Sunni Arabs oppose federalism.
Sunni Arabs were still objecting to the agreement, especially provisions for transforming Iraq into a federal state.
"An agreement between the Shia and the Kurds has been reached ... God willing, the draft will be presented in the parliament today"
One of the top Sunni Arab negotiators, Saleh al-Mutlaq, said he was "surprised by these statements" from the Shia.
"There are still major points of disagreement," al-Mutlaq said.
"I don't think we will reach a solution for them in the next few hours. We are holding talks with the Kurdish brothers and the brothers in the [Shia] alliance and we haven't reached unanimity so far. The meetings are now taking place, and they claim that an agreement has been reached."
Shia and the Kurds have the votes to win parliamentary agreement without the Sunnis.
Iraqi government spokesman Leith Kubba said the minority Sunni Arabs, who were dominant in power under the rule of Saddam Hussein, had still not agreed to the draft.
"The two largest blocs (Shia and Kurds) have agreed to a draft. The Sunnis have to agree to it," he said.
Even if the Shia and Kurds go ahead with the charter without the Sunnis, the minority group can torpedo the whole agreement if their community resoundingly rejects the constitution when it is submitted to a referendum in October.
"There are still major points of disagreement"
Sunni Arab negotiator
That could undercut US hopes that the constitution would lure Sunnis away from violence.
It was not immediately clear if the main stumbling blocks towards agreeing the constitution, federalism, sharing of oil wealth, and the role of Islam - had been resolved or left for discussion at a later date.
Iraq missed an initial deadline last Monday but staved off the need for fresh elections by holding a last-minute parliamentary vote to extend the charter deadline until midnight on 22 August.