Aljazeera learned that the meeting, originally planned for the morning, was postponed until 7pm because of differences among the groups.
Some of the negotiators said agreement had already been reached on almost all issues, but others expressed scepticism.
The initial 15 August deadline was pushed to Monday after no agreement was reached, and Iraqi officials have insisted they would present a final document to the National Assembly, dominated by Shia and Kurds.
Leaders of all three factions initially said they planned to meet for a final round of talks on Monday morning.
Issues holding up agreement on the draft constitution include federalism, distribution of Iraq's oil wealth, power sharing questions among the provinces and the role of the Shia clerical hierarchy.
Vice-President Adil Abdul-Mahdi, a Shia, said 97% of the draft had been completed, and predicted the document would be forwarded to parliament on time.
Government spokesman Laith Kubba said there were two options if political leaders fail to complete the draft: amend the interim constitution again and extend the deadline, or dissolve the parliament.
"I am not optimistic," Kamal Hamdoun, a negotiator for the influential Sunni minority, said on Sunday.
Sunni representatives on the drafting committee appealed to the United States and United Nations on Sunday to prevent Shia and Kurds from pushing a draft through parliament without their consent, warning it would only worsen the crisis in Iraq.
A multi-ethnic demonstration urges
Iraqi unity in the oil city of Kirkuk
They said they were sticking by their opposition to federalism and other demands.
Another Sunni representative, Salim Abd Allah, speaking to Aljazeera from Baghdad, outlined two options if there were to be another delay:
"The National Assembly is dissolved in accordance with the country's administration law for the transitional period, or that the National Assembly demands a further period to be voted[on]."
Abd Allah warned that if the draft constitution did not coincide with the interest of Sunnis, then they would express their frustration on the streets.
Shia and Kurds have enough seats in parliament to win approval for a draft without the Sunni Arabs. But the minority group could scuttle the constitution when voters decide whether to ratify it in the 15 October referendum.
In violence late on Sunday, eight Iraqi police commandos were killed and four wounded in a car bomb explosion at a checkpoint near the suspension bridge in Baghdad's Karada neighbourhood, police said on Monday.
Police also said they had found the bodies of five unidentified men in various parts of Baghdad. All the bodies were handcuffed, bound and shot in the head.
In recent weeks, there has been increasing speculation that death squads, usually referred to as "unknown gunmen", have been operating in many parts of the country.
The US military said on Monday that two soldiers had died when their vehicle overturned during a military operation near Tal Afar, a town 420km northwest of Baghdad.
At least 1868 US troops have died since the Iraq war started in March 2003, according to an Associated Press count.