"The mainstream political parties have dominated the conference and have already drawn up their lists for selecting the national council," said Aziz al-Yasiri, from the National Democratic Movement, a broad coalition interest group, on Tuesday.
"We refuse this and if this is not dealt with today then the whole conference will fall apart and I will walk out, with hundreds with me," added the Shia Muslim from Baghdad, himself nominated for the council.
The threat to walk out comes as a delegation from the conference delayed a visit to Najaf to find a peaceful solution to the fighting there between fighters of Shia leader Muqtada al-Sadr's al-Mahdi Army and US occupation forces.
Some delegation members at the conference said there was also a dispute over whether the vote to select the assembly - which will oversee the interim government until January elections - should take place on Tuesday or when the delegation returned.
The Najaf fighting has dominated the three-day Baghdad meeting of 1300 Iraqi leaders who will select the 100-member assembly. The body was due to be chosen on Tuesday.
"We refuse this and if this is not dealt with today then the whole conference will fall apart and I will walk out, with hundreds with me"
National Democratic Movement
Nineteen of the 100 seats have already been handed to members of the defunct governing council, which was created by the US-led occupation shortly after the fall of Saddam Hussein's government in 2003, and included many figures that had been in exile.
According to conference rules, delegates of different groups - Islamists, secular, Kurdish, Arab or otherwise - are supposed to draw up lists for the remaining 81 seats and submit them to an open vote.
The one gaining a 51% majority would be the winning list.
Once appointed, the assembly will be able to veto legislation with a two-thirds majority, approve Iraq's 2005 Budget, and appoint a new prime minister or president should either resign or die in office.
Despite the apparent pro-government stance of the delegation, the conference has exposed deep divisions over Najaf, with many delegates upset about the fighting.