Mr Balls, a close ally of Mr Brown, said the inquiry, under chairman Sir John Chilcot, was independent and politicians could not dictate whether hearings were in public.
"He (Gordon Brown) said last week that he is talking to Mr Chilcot who is going to do the inquiry. They will decide how they do this," he told GMTV.
"I think that they will be really keen to make sure that members of the public can put their views and former service people as well.
"And if they decide to do some hearings in public then that will be a good thing but that is really a matter for them."
He added: "I think the important thing is that it is an independent inquiry so the guy in charge of the inquiry should decide rather than politicians saying 'you have got to do it this way, or that way'."
His remarks were made after Transport Minister Sadiq Khan yesterday acknowledged the controversy over the inquiry "looked awful" but was partly due to a lack of understanding about the power and autonomy that would be given to Sir John.
It was reported yesterday that former prime minister Tony Blair urged Mr Brown to hold the inquiry in secret.
Mr Brown has faced severe criticism for announcing on Monday the inquiry would be held behind closed doors and was forced into a partial climbdown days later.
After an array of senior figures denounced the decision to hold hearings in private, Downing Street said on Thursday Sir John would have some discretion in how he conducted proceedings.
Mr Khan, Britain's most senior Muslim politician, told BBC1's Politics Show: "I suspect there will be many, many parts of the inquiry held in public."
Asked to admit the situation "did not look good", Mr Khan conceded: "It looked awful. One of the reasons was a lack of understanding of what chairs of inquiries do."
He added: "The terms of reference were set out, from 2001 to 2009, Sir John will decide how his inquiry is held."
Justice Secretary Jack Straw, who was foreign secretary at the time of the 2003 invasion of Iraq, said he would have no objection to giving most of his evidence in public.
He said the indications from Sir John were that it would be "mixed".
The Prime Minister had taken the Franks Inquiry into the Falklands War, which was held in private, as a model, he said.
"That was what the Conservatives had been calling for time after time after time, and they dismissed other inquiries that had been held," he told the Andrew Marr Show on BBC1.
"Now Franks was held in private exclusively. It was for that reason, no other, that Gordon Brown decided to do that."
Mr Straw added: "As foreign secretary at the time I have no problem with giving most of the evidence I have got to give in public."
Northern Ireland Secretary Shaun Woodward said a public inquiry could take years to complete.
He told Sky News's Sunday Live the Saville Inquiry into the events of Bloody Sunday had taken nine years to investigate the events of one afternoon and had cost hundreds of millions of pounds.
"What the public need, and certainly what the MoD needs, is to learn the lessons and learn them fast," he said.
The Observer reported yesterday that Mr Blair pressed the Prime Minister to hold an inquiry behind closed doors because he feared he would be subjected to a "show trial" if it were open to the public.
He is said to have communicated his view to his successor, Mr Brown, via the Cabinet Secretary, Sir Gus O'Donnell. He feared a direct conversation would be leaked, The Observer claimed.
A spokesman for Mr Blair said: "This is a decision for the current Prime Minister, not the former one."
Mr Woodward confirmed Mr Blair had held talks with Sir Gus about giving evidence to the inquiry.
He said: "Of course the Cabinet Secretary discussed this with the former prime minister because he obviously will be one of the major witnesses who will be giving evidence to Sir John Chilcot's inquiry."
Shadow work and pensions secretary Theresa May seized upon the comments made by Mr Khan.
She told the Politics Show: "This is amazing. If it's a Government u-turn and the inquiry is now going to be held in public then I welcome that."
Liberal Democrat leader Nick Clegg said Mr Blair should give evidence to the inquiry in public and under oath.
He said he would be meeting Sir John this week to tell him the only way for the inquiry to have legitimacy is for it to be as public as possible.
Mr Clegg told the Andrew Marr Show: "If the inquiry is to have any legitimacy the prime architect of the decision to go to war in Iraq, alongside George Bush, should give his evidence in public under oath."
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