Last-minute differences between the 25 Council members forced the delay, Hamid al-Bayati, a Council member, told Aljazeera on Friday.
The five Shia members complained over concessions made to Kurds and the makeup of the presidency, said a representative of one of the parties.
Fresh negotiations to try to agree on the interim constitution would resume again on Monday.
The governing council had earlier agreed to the accord unanimously. But Iraq's top Shia cleric, Ayat Allah Ali al-Sistani, rejected provisions put into the text at the Kurds' request, said an unnamed council source.
The move threw a signing ceremony set for Friday into disarray.
The ceremony was put on hold with officials waiting in front of a stage set up in Baghdad's convention centre, 25 fountain pens waiting on an antique desk for the members to use to ink the deal.
"The talks will be resumed on Monday. The issue that we hope to resolve is how to legally codify the transition from a non-elected body to an elected legislature"
Iraqi National Congress spokesman
"The talks will be resumed on Monday. The issue that we hope to resolve is how to legally codify the transition from a non-elected body to an elected legislature," Intifadh Qanbar, spokesman for Ahmad Chalabi's Iraqi National Congress, said.
"There is also the issue of how to protect minority rights," he said.
Al-Bayati, who represents the Shia Supreme Council of the Islamic Revolution in Iraq (SCIRI), said one major point of contention was a clause to approve a permanent constitution once it had been drawn up.
The clause stated even if a majority of Iraqis approved the constitution, it could be vetoed if two-thirds of voters in three provinces rejected it.
The clause was inserted by the Kurds, who run three provinces in northern Iraq and want the power to veto any attempt to rein in their considerable autnomy.
"Some of these provinces have only 400,000 or 500,000 people. We cannot have that number of people rejecting a constitution for 25 million people," al-Bayati said.
The US meanwhile put up a brave face, despite the last-minute postponement being a major embarrassment.
"You are seeing democracy in action," White House spokesman Scott McClellan said.
He asserted that plans to hand over soveriegnty to Iraqis on 30 June would go ahead irrespective of the setback.
Earlier, several mortar rounds hit Baghdad's main airport, hours before Iraqi leaders were due to sign the constitution.
A US army spokesman confirmed six to eight mortars slammed near the airport but there were no casualties.
Friday's roadside bomb left a
crater in the street but no injuries
Police also reported at least one roadside bomb in the Iraqi capital, despite the heightened security and checkpoints in the city.
The interim constitution is expected to become law after the 30 June deadline when US-led occupation authorities hand sovereignty back to Iraqis. The constitution will remain in place until January 2005 elections.
The document lays out the framework for a new administration that will rule over a federal state with two official languages -Arabic and Kurdish.
Comprising more than 60 articles, it enshrines values such as freedom of speech and religion and is an important step in clearing the way for a transfer of sovereignty from the occupation to an Iraqi interim authority.