Less than 90 days before the formal American handover, Mr Bremer is growing impatient.
"We do think there is a role for the United Nations in this process, " Bremer said.
Bush directed Bremer to return to Iraq with proposals on how to accelerate the political transition.
White House officials and Bremer were reluctant to discuss any details of the conversations in public.
Bremer said he believes technology may have played a role, but in a different way.
CNN: Experts: A variety of intelligence factors may have played a role
"We need to find a way to go forward with a transparent and representative fashion, " Bremer said.
But it is quite likely that the compromises reached under Mr Bremer's supervision may harden into permanence.
Feith: This is a subject that is being discussed right now by Ambassador Bremer with the Iraqis.
CENTERFORSECURITYPOLICY: Remarks to the Council on Foreign Relations
Whether Mr Bremer will feel as well disposed towards him a month from now is another matter.
Mr Bremer is also nominating a bevy of general inspectors, one for each ministry, to sniff out corruption.
Ambassador L. PAUL BREMER III National Commission on Terrorism What you have to have in effect is a spy.
But the interim constitution Mr Bremer signed with members of the council is full of caveats favouring the coalition.
"We have to do everything we can to defeat" the insurgents, Bremer said.
Bremer Landesbank has had a rap on the knuckles for doing just that.
Bush also received an update on the situation in Iraq from Franks and Paul Bremer, U.S. civil administrator in Iraq.
John Abizaid, commander of the U.S. Central Command in Iraq and Paul Bremer, the top U.S. civilian administrator in Iraq.
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After meeting Mr Annan, Mr Bremer said he hoped the UN would return to play a role in Iraq soon.
"And you can't get good intelligence against terrorist groups, really good intelligence, without having spies in terrorist groups, " Bremer said.
CNN: Experts: A variety of intelligence factors may have played a role
Paul Bremer, America's top administrator in Iraq, never tires of pointing out that most of the country is improving fast.
He has genuinely taken over many of the decision-making powers previously exercised by the Americans through their now-departed proconsul, Paul Bremer.
The Iraqi soldiers were dismissed from the armed forces in May by Bremer and have received no wages for four months.
CNN: Unpaid Iraqi soldiers start receiving salaries, but discontent simmers
Bremer's British counterpart, Jeremy Greenstock, and John Negroponte, the U.S. ambassador to the United Nations, will also attend the Monday meetings.
In practice, Baghdad was so lawless that Mr Bremer decided to concentrate on law and order rather than on introducing democracy.
In brief remarks to reporters, Bush said his meeting with L. Paul Bremer, the U.S. civilian administrator in Iraq, was fruitful.
However, under pressure from Iraqi politicians, Mr Bremer agreed last November to bring forward the transfer to self-rule to this month.
Now, Ambassador Bremer was rushed back to Washington for these urgent consultations.
And this leads to the challenge for L. Paul Bremer, the top U.S. official in Iraq, who's off to a good start.
"We are in the process of trying to establish the best way to arrive at a fully representative interim administration, " Bremer said.
Some threaten to scrap Mr Bremer's edicts as soon as he goes.
It would not be a "provisional government, " Bremer said, noting the U.N.
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