The US president, George Bush, summoned his top official in Iraq, Paul Bremer, for urgent talks on how to salvage the plan to hand over authority to an interim Iraqi government by June 30.
It was thrown into disarray last weekend when Iraq's leading Shia cleric, Grand Ayatollah Ali Sistani, said that unless the government was directly elected by the people violence would get worse.
Mr Bremer emerged later to say that while the June deadline was set in stone, the administration was open to modifying the process by which representatives were chosen.
"There obviously are a number of ways in which these kind of elections can go forward," Mr Bremer said, adding that the nationwide direct elections Ayatollah Sistani favoured would be premature.
Mr Bremer is expected to urge the UN secretary general, Kofi Annan, to send a team to Iraq to convince the Shia community that elections were not yet feasible.
The US was meanwhile facing another headache when it emerged yesterday that its commander in Iraq had ordered an investigation into reports of abuse of Iraqi prisoners. Rights groups have accused coalition forces of harsh treatment of some of the 13,000 detainees still being held.
The US idea to transfer power back to Iraqis is for caucuses of the "great and the good" in 18 provinces to choose a transitional government by June 30.
The Shia, who make up 60% of Iraq's population, want direct elections because they could expect to emerge as the dominant group.
Ayatollah Sistani's potential to derail the transition process was confirmed on Thursday when tens of thousands of Iraqis took to the streets of Basra chanting, "Yes, yes, to Sistani; no, no to selection!"
"We are neither so stupid nor so reckless as to want to make an enemy of Ali Sistani," a senior US official told the Los Angeles Times.
The Foreign Office signalled yesterday that it was keen to move towards Ayatollah Sistani's proposals, but only if a workable method of holding a direction election could be found.
The foreign secretary, Jack Straw, speaking on BBC Radio 4's World At One, insisted that it was important that in any arrangement the rights of the minority Sunnis were safeguarded. He said: "Across Europe you have got countries like Belgium and Switzerland where you have potential for very significant nationalist rivalries; and yet, by a process of careful drafting and practice of their constitutions, they have been able to balance this.
"The result is, yes, a majority is a majority, but minority rights are protected. Now that is the kind of architecture that has to be developed in Iraq."
As well as seeking the help of the UN, the Bush administration is also considering an appeal to those European nations (notably France, Germany and Russia) it had snubbed for opposing the war, by withdrawing a ban on their right to bid for contracts to rebuild Iraq.
"I've heard people back-pedalling all over the government on this," one US official said.
In Paris, the foreign minister, Dominique de Villepin, did not rule out sending French troops to Iraq at a later date. "We shall have the opportunity to look in detail at this when a government has been formed in Iraq," he said.
The US climbdown has been prompted by domestic considerations. The transfer of some powers to a transitional government had been scheduled to be completed by July 1, four months before the US presidential election. This has put the UN, which left Baghdad in August after its headquarters was bombed, in a strong bargaining position.
"It's clear we want the UN involved," an administration official told the New York Times. "It's clear the Iraqis want them. It's clear the security situation has improved, and we're willing to help with their security. But there are many stages we have to go through to get an agreement."
However, the UN is also in a quandary. Mr Annan, who meets Mr Bremer and Iraqi officials on Monday and who agrees that early elections would be premature, is keen to play a political and humanitarian role in the process. But he is reluctant to lend the UN's imprimatur to what many UN officials believe is a makeshift process owing more to Mr Bush's re-election than stability and security in Iraq.
"This meeting for us is a step along the way," said an aide to Mr Annan. "We're going to listen to what they have to say, reflect on what they expect of us, and get more detail on exactly how these caucuses are going to run."