The chairman of the meeting to pick the assembly Fuad Maasum said on Tuesday, independent and non-governmental delegates would be allowed to submit their own candidates on Wednesday.
Delegates apparently protested against the candidates Maasum presented at the conference being handpicked by the pro-US appointed interim government.
"We will vote tomorrow. It's getting too late because if we stay here they will not let us leave the building after midnight," he said, telling delegates to return on Wednesday at 10:00am (0600 GMT).
Independent delegates have criticised the conference as being stacked by officials and government delegates, saying the assembly due to be chosen to oversee the interim government could amount to a rubber stamp.
About 450 delegates at the conference accused the main political parties of hijacking the vote, saying most members were chosen long ago in secret.
Many had threatened to quit the conference unless the voting mechanism was changed.
But Maasum suggested that one list be put to the vote, saying "the idea of one list was crucial to maintain balance and accord".
Of the 81 seats on the interim legislature to be decided by the vote, 21 are to go to party members, 21 to provincial leaders, 11 to minorities, 10 to tribal figures, 10 to civil society organisations and eight to independents.
Maasum, a Kurdish politician and former exilee, insisted the process had been fair.
Aljazeera's correspondent in Iraq says the procedure will follow the United Nations model of voting.
Members of the defunct governing council, appointed by the US-led occupation authority have an automatic right to sit on the legislature, bringing its membership up to a total of 100, 25 of whom are to be women.
Nineteen seats are, however, reserved for members of the defunct Council on the assembly, which will also have a role in organising elections due by January.