The announcement, from the National Assembly's top spokesman Bishro Ibrahim, came as negotiators struggled to find consensus on a draft charter that Shiite and Kurd representatives have accepted, but Sunni Arabs still oppose.
Sunni opposition derailed a vote Monday night, at which time assembly Speaker Hajim al-Hassani said three more days of talks would be held to try to bring the Sunnis on board.
Sunnis, who are an ethnic minority that for generations controlled the government of Iraq, are opposed to a constitution that includes federalism, which would set up powerful local regions rather than a strong central authority.
After the announcement was made, President Jalal Talabani expressed some optimism that an agreement would still be reached.
"Efforts are still continuing to reach consensus in the coming hours," he said at a joint conference with a Sunni leader, adding that Sunnis should get a larger role in drafting the constitution, reported the New York Times.
It was unclear if a formal parliament vote would even be necessary. Shiite representative Khaled al-Attiyah said there was no need for an assembly vote because the constitutional committee met its legal obligations by delivering a draft by the Aug. 22 deadline, according to the Associated Press.
Another Shiite, Nadim al-Jabiri, said there would be no vote Thursday because the draft will be approved or rejected in a referendum Oct. 15.
Under rules agreed to last year, the National Assembly is obligated to dissolve itself and hold new elections if it is unable to come to consensus on the interim constitution. If voters reject the referendum, the assembly will dissolve and the process will start from scratch.
Before the assembly called off its meeting Thursday, rebel Shiite cleric Muqtada al-Sadr urged his followers to end clashes with Shiite rivals. A day earlier, his office in the holy city of Najaf was burned and four of his supporters were killed, reported the AP.
He urged "all believers to spare the blood of the Muslims and to return to their homes."
"I will not forget this attack on the office ... but Iraq is passing through a critical and difficult period that requires unity," he told reporters in his home in Najaf, according to the AP.
Al-Sadr demanded that Abdul-Aziz al-Hakim, leader of the rival Supreme Council for the Islamic Revolution in Iraq, or SCIRI, condemn "what his followers have done."
SCIRI has denied any role in the attack.