Members of Iraq's interim Governing Council have called for "nothing less than full sovereignty" after the planned transfer of power on 30 June.
US and Iraq officials agree that security co-operation is needed
US Secretary of State Colin Powell has said Iraq would have to "give back" some power to the US in the early days.
That caused concern among Iraqi leaders and on the United Nations Security Council which is expected to be asked to support the new government in Iraq.
UN envoy Lakhdar Brahimi later told the Council the role of Iraqis was vital.
He said the people of Iraq should be as involved as possible in forming the interim government which will administer the country until full elections, due in January next year.
Mr Brahimi favours the winding up of the 25-member Governing Council appointed by the US from veteran politicians to be replaced by technocrats.
He also suggested a national conference of more than 1,000 Iraqis from all walks of life be held in July.
That could offer support and advice to the government as it prepared for elections and act as a forum for reconciliation in the post-Saddam Hussein era, he said.
The BBC's Middle East analyst Roger Hardy says it is clear that the US will remain the dominant power in Iraq in both military and financial terms for some time to come.
But he adds that the US has have to convince ordinary Iraqis that what is being billed as the handover of power will not be a purely symbolic moment.
Mr Powell's comments - which came a week after US administrator for Iraq Paul Bremer said local Iraqi forces could not maintain security by themselves - were criticised swiftly by Iraqi politicians.
A spokesman for the Iraqi Governing Council, Hameed al-Kafaei, said he believed Mr Powell was talking about co-operation over security.
"But sovereignty will have to be full on 30 June. Iraqis will not accept any less than full sovereignty," he said.
Public Works Minister Nesreen Berwari told the Associated Press news agency that Iraqis would welcome support for security and building democratic institutions from the UN and the US.
But she said Iraqis must take control of local and national government and make decisions on "day-to-day life," including budgets and "how to move the country politically".
As the members of the Security Council prepared to hear Mr Brahimi's latest report in New York, the only Arab member of the Council also called for Iraq to have full control after 30 June.
Algerian UN Ambassador Abdallah Baali said: "We definitely would like to see the Iraqi sovereignty restored in full and as soon as possible."
UN 'leading role'
Separately, the former US Ambassador to the UN, John Negroponte, was being questioned by senators deciding whether to approve him as the White House's new envoy in Iraq.
Mr Negroponte told the Senate Foreign Relations Committee that he expected the UN to take the lead in post-transition Iraq, in particular as it moves towards rule by an elected government.
Mr Negroponte said Iraqis might take over roles before 30 June
If his appointment is confirmed, Mr Negroponte will replace Mr Bremer as the top US civilian in Iraq after 30 June when Mr Bremer's Coalition Provisional Authority ceases to exist.
But US officials have said their military forces will still have control of some aspects of security and Mr Powell went further on Monday, saying that while Iraqis would have what he called sovereignty, "some of its sovereignty will have to be given back... or limited by them".
He told Reuters news agency that the coalition did not mean to "seize anything away" from the planned caretaker government but added: "It is with the understanding that they need our help and for us to provide that help we have to be able to operate freely, which in some ways infringes on what some would call full sovereignty."
White House spokesman Scott McClellan said on Tuesday that it was important to separate "sovereignty" from "authority".
He said Iraqis themselves wanted limits on the authority of the interim government which he said had just two roles before it is replaced by an elected body: to assume day-to-day responsibility for administration and to prepare the country for a national poll.