Lord Falconer says the war is "one of the major events in British politics"
Former cabinet minister Lord Falconer has joined calls for the Iraq inquiry to be held "largely" in public.
The ex Lord Chancellor told BBC One's Question Time: "If it is not done in public, then people will not have confidence in relation to the inquiry".
Downing Street said on Thursday that Prime Minister Gordon Brown did not object to public sessions.
Mr Brown initially said the inquiry would be held in private - sparking widespread criticism.
He said the inquiry would hear evidence in private so witnesses could be "as full and as candid as possible".
But pressed on Thursday about the growing calls for it to be held in public, the prime minister's official spokesman said it would be up to inquiry chairman Sir John Chilcot to "consider how the precise format of the inquiry should be structured to ensure that the objectives are met".
Lord Falconer, formerly one of Tony Blair's closest allies in government, who was drafted into the cabinet in the period after the invasion of Iraq, conceded that some aspects may have to be held in private on grounds of national security.
But he added: "I think the Iraq war is one of the major events in British politics - if we are going to have an inquiry at all, then I think it's got to be largely in public."
Meanwhile, Alastair Campbell, who was director of communications at Number 10 when the Iraq conflict began, has said it "frankly won't make any difference" to critics of the war if the inquiry was held in private.
At a fund-raising event at the House of Commons on Thursday night, Mr Campbell said opponents of the conflict had already made up their mind, whatever comes out of the inquiry.
The prime minister has told the chairman of the inquiry, Sir John Chilcott, that he can decide to hold public sessions if he chooses.
Gordon Brown had written to Sir John to say that the families of those who died in Iraq may wish to give evidence and it would be up to Sir John to decide at their request whether to hold public sessions, his spokesman said.
Mr Brown had also asked Sir John to consider whether witnesses would give evidence under oath.
A growing number of public figures have called for the inquiry to be in public, following the prime minister's statement on Monday.
Former Conservative prime minister Sir John Major said the findings risked being denounced as a "whitewash" and said the decision to hold it in private was "inexplicable".
General Sir Michael Jackson, who was head of the Army during the 2003 Iraq invasion, told the BBC it "must be open wherever possible".
Lord Butler, a former cabinet secretary who headed a 2004 inquiry into the use of intelligence in the run up to the Iraq war also called public hearings.
He told peers: "I reluctantly conclude that the form of the inquiry proposed by the government has been dictated more by the government's political interest than the national interest and it cannot achieve the purpose of purging mistrust."
Both the Conservatives and the Liberal Democrats have been pressing for some hearings to be held in public.
MPs will debate a Tory motion next week calling for the inquiry's proceedings to be held in public "whenever possible".
The inquiry will cover the period from July 2001 to July 2009. Hearings will start next month and take at least a year.