The prime minister is facing growing pressure to say the basis for going to war in Iraq was flawed.
Opposition MPs have called for a public inquiry
Ex-minister Robin Cook said Tony Blair should use the Hutton report to set the record straight on the issue.
The Tories and Liberal Democrats want a public inquiry into the case for war.
Mr Blair insists weapons of mass destruction will be found although the official leading the US search resigned saying they did not exist.
Former foreign secretary Mr Cook told the BBC Mr Blair had been driven to war by "missionary zeal" and the desire to show loyalty to US President George W Bush.
After resigning, US search official David Kay said he did not believe there had been large-scale production of chemical or biological weapons in Iraq since 1991.
On Saturday US Secretary of State Colin Powell said Iraq may not have possessed any stockpiles of weapons of mass destruction before the Iraq War.
Mr Cook, who resigned in protest at the prospect of war with Iraq, told BBC Radio 4's Today programme it was "rather undignified" of Mr Blair to continue to insist he was right when "everybody could now see he was wrong".
"It is very important that Tony Blair does concede that there were mistakes made, maybe in all good faith.
"If there was no threat from Iraq we obviously had no right to carry out a pre-emptive strike to remove that threat. And we better drop that doctrine before somebody else in the world uses it in their own back yard."
Mr Cook said he did not believe Mr Blair was trying to deceive, but was "behaving in a way which had a missionary zeal, an evangelical certainty."
"The reality is that Number 10 was keen to get into the war, not frankly because they were particularly concerned about WMD - I suspect by March they also knew that the September document had over-egged the case - they were keen to get in to impress President Bush that they were a reliable ally."
Shadow foreign secretary Michael Ancram and Liberal Democrat foreign affairs spokesman Menzies Campbell have called for a public inquiry into the case for war.
Mr Ancram said: "It is important if we are to be able to rely... on the word of the prime minister in relation to intelligence, that we now find out what the basis of his comments were."
Liberal Democrat foreign affairs spokesman Menzies Campbell said: "It is pretty extraordinary that first Hans Blix... David Kay and now David Kay's successor have all effectively said the same thing."
Downing Street said Mr Blair was still confident Saddam Hussein had weapons of mass destruction and that evidence would be found.
"There is still more work to be done and we should await the conclusion of that work," said a spokesman.