Meetings were to resume on Wednesday among Iraqi leaders seeking to finish the draft by the new 22 August deadline.
Iraqi leaders expressed confidence on Tuesday that they would overcome differences over remaining issues, including Kurdish demands for self-determination and the role of Islam, by Monday.
However, many leaders were equally sanguine about prospects for meeting the original 15 August deadline. If no agreement can be reached this time, the interim constitution requires that parliament be dissolved.
Different groups gave conflicting information on what had been resolved and what stood in the way of a deal.
Role of Islam
Shia lawmakers cited the role of Islam - an issue that affects women's rights - and self-determination for the Kurds, which Arabs fear would mean they would eventually secede from the country.
President Jalal Talabani, a Kurd, insisted the Islam issue had been solved and "you will see in the constitution that it is not a problem".
Prime Minister Ibrahim al-Jaafari, a Shia, mentioned federalism, the election law and the formula for distributing revenue from oil and other natural resources.
Iraqis are worried about divisions
seen in the country's leadership
Sunni negotiator Muhammad Abed-Rabbou said "the most important point is federalism".
Most also cited Kurdish demands for self-determination - a step beyond federalism because it would imply the right to break away from Iraq.
US ambassador Zalmay Khalilzad insisted that self-determination was "not on the table".
Talabani, leader of the Patriotic Union of Kurdistan, acknowledged that his fellow Kurds wanted self-determination but brushed aside talk of secession.
"There are rumours that the Kurds want to secede, but they are for unity," he said on Tuesday.
Other Kurds defended their self-determination demand, but also said they had no plans to secede.
Kurdish Democratic Party.
"Kurdish politicians have no present intentions to gain independence. But we need self-determination in order to decide our future in case troubles erupt in Iraq in the future," said Mullah Bakhtiyar, a senior official in the
"We are not making surprise or sudden demands, it is the Shia who are doing so," said Bakhtiyar. He also said Shia were pressing to grant special status for their clerics.
Al-Jaafari said the differences
were mostly over details
Bakhtiyar said such special status would be "a dangerous thing because every sect will seek orders from its religious leadership and this means that there will be no rule by law or constitution".
Al-Jaafari said disagreements were largely over details and he expressed confidence that Iraq's constitution could be finished within a week.
"I hope that we will not need another extension. The pending points do not need too much time and, God willing, we will finish it on time," he said on Tuesday.
President Talabani added that he expected the constitution to be finished "before the deadline".
The delay was an embarrassment for the Bush administration, which insisted that the original deadline be met to maintain political momentum and blunt Iraq's deadly uprising.
The US military announced on Tuesday that three American soldiers were killed the night before when their vehicle overturned during combat operations in south Baghdad.
At least 15 Iraqis were killed on Tuesday in Baghdad and central Iraq in anti-US presence operations.
If agreement on a constitution is reached, Iraqis will vote around 15 October to accept or reject the charter, leading to more elections in December for the country's first fully constitutional government since the US-led invasion toppled Saddam Hussein's government in 2003.
Kurdish leaders say they have no
plans to split from Iraq
Khalilzad, the US ambassador, sought to downplay the delay, adding that he was convinced a deal could be reached by the new deadline.
"I believe that an agreement will be arrived at if the leaders continue with the attitude of compromising, putting oneself in the shoes of the other side," Khalilzad said in Baghdad.
The United States hopes political progress, including adoption of a democratic constitution, will help deflate the uprising and enable the Americans and their partners to begin withdrawing troops next year.
Nevertheless, the last-minute decision to postpone the deadline has raised serious questions about the ability of Iraq's varied factions to make the necessary political compromises.
Some Iraqi citizens were worried about the exposed fractures in the country's leadership.
"We are disappointed because we risked our lives when we went out to polling stations, but now we see each political bloc searching for its own interests," said Taha Sabir in Baghdad.
"We expected a better life, but we got only many crises such as electricity and fuel shortages."