The Prime Minister's spokesman said that it had never been "an issue of theology" for the Government whether hearings were held in the open or behind closed doors.
He said that it would be up to the inquiry chairman Sir John Chilcot to decide how the inquiry should be structured in order to achieve its objective of establishing the truth of what happened.
He stressed however that the Government did not want to see a lengthy public inquiry like the Saville Inquiry into the Bloody Sunday killings which went on for years involving "countless lawyers".
In a letter to Sir John, Gordon Brown said it was essential witnesses to the inquiry were able to give evidence with "the greatest possible candour and openness" while maintaining "full public confidence in the integrity of the process" and not damaging national security.
"Once you have met, as I have suggested, the leaders of the other political parties and the chairs of the relevant parliamentary select committees it would be helpful if you could set out how you and your colleagues think these objectives can best be met in the way that the inquiry is conducted," he said.
Mr Brown said he hoped Sir John would consider whether it was possible for witnesses to give evidence on oath.
He suggested Sir John and his inquiry team should meet the relatives of the service men and women who had died in Iraq - either in public or in private - to explain how the inquiry would operate.
He also urged Sir John to hold an open session to "explain in greater depth the significant scope and breadth of the inquiry".
Mr Brown disclosed he had written to all relevant current and former ministers to "underline the importance of their full cooperation".
Meanwhile, Cabinet Secretary Sir Gus O'Donnell was writing to Government departments informing them of the need for "full transparency".
Mr Brown's intervention came amid growing criticism by senior military figures over the decision announced by the Prime Minister on Monday that all the inquiry hearings would be held behind closed doors.
Lord Butler of Brockwell, the former cabinet secretary who led the last official inquiry into the Iraq war, was reported to be preparing to use a House of Lords debate later today to accuse the Government of "putting its political interests ahead of the national interest".
The Prime Minister's spokesman said the Government "completely reject" the charge.
The spokesman said it would now be for Sir John and his team to consider exactly how they wanted to proceed.
The question of whether some of this might be in public has never been an issue of theology for us," the spokesman said.
"This is not some protracted Saville-type inquiry that goes on for years involving countless lawyers.
"I think it will be up to Sir John to consider how the precise format of the inquiry should be structured to ensure that the objectives are met.
"The issue for us has always been to ensure that the inquiry is structured in a way that gets to the truth and people are able to speak honestly and candidly about how decisions were taken."
The head of the Army, Sir Richard Dannatt, disclosed yesterday that he had not been consulted on the format of the inquiry and said he saw "a lot of merit" in holding some hearings in public.
His predecessor, General Sir Mike Jackson, who was head of the Army at the time of the invasion of Iraq in 2003, has said he would be happy to give evidence in public and warned closed hearings would simply feed the current climate of suspicion about Government.
Lord Scott of Foscote, the law lord who carried out the arms-to-Iraq inquiry in the 1990s, backed calls for the evidence to heard in public, with a provision for the inquiry to go into closed session when necessary.
"It almost certainly shouldn't entirely be held in public, as there's bound to be some of the evidence that shouldn't be heard in public," he told BBC Radio 4's The World at One.
"But as a general proposition, I take the view that an inquiry, the purpose of which is to allay public disquiet about some event in which the Government or the state has been involved, is not going to achieve its purpose unless it is broadly speaking held in public."
Gen Jackson meanwhile questioned the lack of any senior military figure on the inquiry team.
"I am surprised that the panel does not include a senior military figure, he would obviously have to be retired, in order to ensure that the panel fully understands the military dimension," he told the World at One.
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