He is to outline how the interim government, which is to take over on 30 June, will work.
Continued fighting against the cleric Moqtada Sadr in the holy cities of Karbala and Najaf.
President Bush's aims
Mr Bush will want to show in his speech that all this has to be balanced against the more encouraging prospect of a handover of authority from the coalition to an interim Iraqi government on 30 June.
Mr Bush will try to demonstrate that he is not a passive onlooker, but can exert some influence.
At the same time, however, the former senior British official in Iraq has suggested that the test of whether Iraq will achieve stability will come not from the handover but from elections due in December or January.
It is a sign of the uncertainty surrounding coalition policy that the handover is being promoted as a watershed, and at the same time is being downplayed as merely a shift to a caretaker administration.
What was once planned as an orderly transfer of power in Iraq over a period of months in an atmosphere of peace and co-operation is now a race against violence and chaos. What once looked like sensible planning now looks like muddle.
The British official, Sir Jeremy Greenstock, who was Britain's senior representative in the Coalition Authority in Baghdad until recently, told the BBC: "What we are really looking towards in the next few months is not what happens in the interim government, but in elections for a national assembly... that will be the real test."
So Sir Jeremy is trying to extend the timeline of expectation from the interim government of 30 June, to the government which will emerge from the assembly elections early next year.
That leaves another six months of uncertainty.
No names
In order to tackle this uncertainty, the US and UK are trying to bolster the influence of the interim government as far as they can.
It will have no power to make or change law, but increasingly the one area where it might exercise some authority is security - that means control in some way of the security forces both Iraqi and foreign.
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It is a time of great nervousness, amounting to panic almost in some quarters, about the way Iraq has gone out of control
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Recently a senior British official said the Iraqis would probably have to have an opt-out from military operations.
He compared this to the position during the Kosovo war when a British general refused to confront Russian forces despite being ordered to do so by the American commander. The British officer appealed to London and was allowed to refuse to carry out the order.
Sir Jeremy Greenstock went further and said the interim government "has got to be responsible for security in terms of policy... that is going to be Iraqi".
The interim government has not yet been named.
Efforts to get agreement among Iraqi political leaders are being led by the United Nations envoy Lakhdar Brahimi, but it is unclear whether he will select technocrats as he originally suggested or a more forceful political line-up which might provide more leadership.
The interim government will have a three-person presidency plus a prime minister who will be the key figure. Under him, ministers will be appointed to the various ministries.
This government will hold office only until the assembly elections. Then the assembly will appoint a transitional government. It will not be until the end of next year that a directly elected government will be formed.
'Thumbs up'
The US and UK are also seeking a new UN resolution to get international approval for the arrangements.
The US has been training a new Iraqi security force
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President Bush's speech on Monday will be followed by others in the run-up to 30 June.
He has also been rallying support among Republicans in Congress with a visit to Capitol Hill on Thursday.
After the meeting, Senator John McCain, once his rival for the presidency, gave the thumbs-up and said Mr Bush had made a good speech.
It is a time of great nervousness, amounting to panic almost in some quarters, about the way Iraq has gone out of control. But nobody thinks the end is in sight.