There were 22 killed in the August attack on the UN HQ
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White House officials say the United Nations is to be asked to go back into Iraq to help oversee the transfer of power to the Iraqis.
The US will try to persuade the UN Secretary-General, Kofi Annan, to back the plan to set up an unelected government in Iraq by July.
The spiritual leader of Iraqi Shias, Ayatollah Ali al-Sistani, is demanding direct elections first.
The UN pulled out of Iraq after a huge bomb attack on its offices in August.
Mr Annan has said the UN could help but only if given a role commensurate with the risks involved.
The American administrator, Paul Bremer, will meet Mr Annan on Monday.
'Refinements'
The BBC's Justin Webb says the US can't sure whether Mr Annan will back the American process or the timetable the US has chosen.
He says it seems the White House is willing to offer incentives to key members of the UN Security Council to get them involved.
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We will see protests, strikes and may be clashes with the occupation troops if they insist on their colonialist scheme
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US officials say the ban on French and Russian companies bidding for contracts in Iraq could be lifted.
After talks with President Bush on Friday, Mr Bremer said he was ready to make what he called refinements to the plan to set up an unelected government in Iraq, but he doubted direct elections could be held before the July deadline.
Mr Bremer echoed that view, saying: "We've always said we're willing to consider refinements and that's something that we will be willing to discuss at the appropriate time."
The meeting in Washington came a day after a mass demonstration in the southern city of Basra in support of the demands of Ayatollah Sistani.
Correspondents say the support of Shias is vital for any new Iraqi government to have legitimacy.
Shias were long repressed by Saddam Hussein and they want more open elections to reflect their numerical superiority, correspondents say.
Fatwa warning
The strongest challenge yet to the coalition came during Friday prayers in the holy city of Karbala from Sheikh Abdul Mahdi, the local representative of Ayatollah Sistani.
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POWER TRANSFER TIMELINE
Feb 2004: Fundamental Law (provisional constitution) to be introduced
May, 2004: Selection of Transitional National Assembly (TNA)
June 2004: TNA to take power; Coalition Authority and Governing Council to dissolve
March 2005: Constitutional Convention elected to draft new constitution
Dec 2005: New constitution; elections and appointment of new government
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He told followers: "In the next few days, we will see protests, strikes and may be clashes with the occupation troops if they insist on their colonialist scheme and on
designing Iraq's policy according to their own interests."
The BBC's Dumeetha Luthra in Basra reports that another Sistani aide said the ayatollah could issue a fatwa, banning co-operation with coalition forces.
On Thursday Hojat al-Islam Ali Abdulhakim al-Safi, the second most senior Shia cleric in Iraq, sent a letter to President Bush and UK Prime Minister Tony Blair accusing them of delaying full elections to serve their own purposes.