The United Nations' special envoy has called for an interim Iraqi government to be named before the end of May.
Mr Brahimi said security was still a key concern across Iraq
The caretaker president and his team would then have a month to prepare for the 30 June handover of power, Lakhdar Brahimi told the Security Council.
His comments came as Iraqi politicians expressed concern that the US would not return "full sovereignty" in June.
US Secretary of State Colin Powell has said Iraq would have to "give back" some power to the US in the early days.
'Time is short'
Mr Brahimi reported to the United Nations in New York following a visit to Iraq earlier this month.
"There is much to do and time is short," he told the meeting of the 15-member Council which was also attended by UN Secretary General Kofi Annan.
By 31 May: Identify members of caretaker government, including president and two vice-presidents
30 June: US-led coalition hands power to interim government as scheduled
July: Hold a national conference to aid Iraqi reconciliation and identify way forward
Mr Brahimi stuck to his views that non-political technocrats should form the caretaker administration which will run Iraq until an elected government is formed after national polls due by the end of January 2005.
He called for an interim president, two vice-presidents, a prime minister and the rest of the team to be announced by the end of May, to help to demonstrate that the handover was more than symbolism and to give the officials time to become acquainted with their new roles.
"It would be best if the members of the caretaker government, including the president and vice-presidents, were not to stand for election," he said.
But while the interim government would, by definition, have a limited role, there should be the beginnings of a much broader, national debate about the future of Iraq.
Mr Brahimi said the UN could help to identify between 1,000 and 1,500 Iraqis from all walks of life to form a national conference in July.
The delegates from all provinces, political parties and religions in Iraq as well as representatives of trade and professional sectors, women's groups, universities, writers and poets could offer support and advice to the government as it prepared for elections, he said.
It could also act as a forum for national reconciliation.
"For the last three decades, Iraqis were not communicating with each other," he said.
Mr Brahimi, who was also Mr Annan's special envoy on Afghanistan after a US-led invasion overthrew the Taleban there, said that the job in Iraq was "do-able".
Mr Brahimi described the security situation in Iraq as "extremely worrying", but said the absence of a credible Iraqi government was a major cause of the instability.
He said the international community had little option but to try to make progress.
The Security Council meeting adjourned without discussion of Mr Brahimi's report.
Earlier, the US Ambassador to the UN, John Negroponte, told the US Congress that he expected the UN to take the lead in post-transition Iraq, in particular as it moves towards rule by an elected government.
He was being questioned by the Senate Foreign Relations Committee over his nomination to be the US ambassador to Iraq who will become the top US civilian there when Paul Bremer's Coalition Provisional Authority ceases to exist at the handover of power.
US and Iraq officials agree that security co-operation is needed
But the post-handover of the US has been causing concern following comments by Mr Powell and others that the US will continue to take responsibility for security and other areas.
A spokesman for the Iraqi Governing Council, Hameed al-Kafaei, said: "Iraqis will not accept any less than full sovereignty."
The only Arab member of the UN Security 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."