A spokesman for the Iraqi government has said that political leaders have agreed some amendments to the draft constitution in an effort to reach a consensus.
An earlier deadline was extended for three days to try to secure consensus among the three main groups, Shias, Sunnis and Kurds.
Sunni Arab leaders have raised objections to on several key issues, including the extent of federalism.
36 bodies found in river
Meanwhile, Iraqi police say they have found the bodies of 36 men shot dead and dumped in a shallow river south of Baghdad. A senior officer said the victims were killed by a single bullet to the head.
In another incident north of Baghdad, gunmen shot dead two bodyguards of the Iraqi President Jalal Talabani and wounded seven others.
President Talabani was not in the convoy at the time of the attack.
Civilians gunned down in café
Earlier, six Iraqi civilians were killed and 15 wounded when gunmen burst into a popular café north of Baghdad and opened fire.
The attack took place in the small town of Abu Sayda, about 60km north of the Iraqi capital.
Health officials said people, mostly elderly men, had gathered at the café for breakfast before gunmen sprayed them with gunfire.
It was not immediately clear who was behind the attack but survivors said they suspected Muslim militants, who are part of an insurgency seeking to topple the US-backed government with a relentless campaign of suicide bombings and shootings.
Iraqi government officials accuse Muslim militants and insurgents loyal to former leader Saddam Hussein of also carrying out indiscriminate attacks that have killed civilians.
