International observers say the revised law is vital to the process of democratising Iraq
Iraqi MPs say they are not yet ready to pass an election law that needs to be approved urgently if polls are to be held on schedule in January.
The UN had warned that it could not guarantee to endorse the polls if the bill was not approved on Sunday.
MPs have told the BBC that the vote might not be held for several days as several sticking points remain.
There are fears that delaying the election could undo recent progress towards greater stability in Iraq.
The poll is seen as crucial to the stability of the country, and any delay could impact on the US plan for withdrawal.
The Obama administration wants to pull all its combat troops out by the end of August next year, in preparation for a full military withdrawal by 2012.
2003: US appoints Governing Council
2004: Governing Council elects interim government
Aug 2004: National conference elects interim national assembly
Jan 2005: First general elections for transitional national assembly and provincial councils - Sunnis boycott vote
Dec 2005: General elections for first full-term government and parliament
Jan 2009: Elections for provincial councils - key test of security gains
Jan 2010: General elections due
The electoral law is meant to be in place at least 90 days before voting takes place, and Iraq's election body says it needs to be adopted by Tuesday.
Pressure from the UN, the US and Iraqi political and religious leaders has so far failed to break the deadlock in the Iraqi parliament.
MPs say the UN has proposed a compromise to the main sticking points - on how candidates are listed on the ballot paper and the distribution of seats in the ethnically divided, oil-rich city of Kirkuk.
Sunday saw a series of separate bombings across Iraq kill at least eight people.
In the deadliest attack, five people were killed and 37 wounded when a bomb hidden in a cooler on the back of a bicycle exploded at a market in southern Babil province.
Meanwhile, government officials have said repairs to ministry buildings hit by massive bombings in the centre of Baghdad last week will cost about 19 million dollars ($16.3m).
The twin suicide bombings in the capital killed more than 150 people.