Talks between the parties have been taking place for weeks now and participants say an agreement on the administration's powers and make-up is close.
"We will be able to hammer out an agreement by mid-July," Adel Abdul Mahdi of the Supreme Assembly of the Islamic Revolution in Iraq (SAIRI), the main Shia Muslim group said.
"We do not accept that this council should have a purely advisory role, and the Americans concur with us on this," he said.
"The council will nominate ministers, oversee their work and define political guidelines," according to the SAIRI official.
Mahdi said the interim body would represent various components of the Iraqi population without necessarily reflecting the weight of each political group.
But Mahdi said there were differences concerning the way the larger 125-member assembly, which would be charged with drafting the constitution, will be selected.
"This is a delicate issue. The members of the assembly must be elected, and the constitution must be endorsed in a referendum," he said.
The occupation authority has ruled out elections at this point.
Muhammad Tawfiq, an official of the Patriotic Union of Kurdistan (PUK), one of the two main Iraqi Kurdish parties, said he did not think the demand by Shia religious authorities for elections to pick the members of the assembly that will draft the constitution was practical.
"How can the nation go to the polls when there is no government and no population census?" he asked.
The US has been under pressure to transfer power to the Iraqis and the formation of the administration would be a first step.
In Hungary, visiting Russian Foreign Minister Igor Ivanov said Moscow would like to see the setting up of a legitimate government composed of Iraqis as soon as possible.
The US occupation administration has also been trying to set up a new Iraqi army after ousted President Saddam Hussein's military was dissolved.
US administrator Bremer said Tuesday he expected training into the new army would start by the middle of this month.
The army - intended to become 10,000-strong within a year - would be "motorized, lightly armed, largely directed at defending Iraq's borders ... It will not have internal security duties," he told reporters in Baghdad.
A Kurdish newspaper Khabat meanwhile reported on Wednesday 48 fighters from the Kurdistan Democratic Party (KDP) have gone to the northern city of Mosul to receive training by US forces that will enable them to join the new army.
The KDP and the PUK which have controlled Iraqi Kurdistan since the end of the 1991 Gulf War, together command more than 50,000 peshmergas, a number that doubles if reservists are counted.
Officials from both sides have said they hope their men will be integrated into a reconstituted army.
They expect Kurds to be given the task of guarding Iraq's borders and other duties inside Iraqi Kurdistan.
Fighters of the KDP and PUK, both of which allied themselves with US and British forces, were exempted from an order to Iraqi militias to lay down their weapons by mid-June.