An independent inquiry is to examine intelligence which led Britain to war over Iraqi weapons of mass destruction.
Tony Blair was grilled for two-and-a-half hours
Former cabinet secretary Lord Butler will chair a five-member committee looking at whether the pre-war intelligence was right or wrong.
The committee will include two MPs, but the Lib Dems are not taking part - because it will not look at the political judgements on the war.
Earlier, Tony Blair said the inquiry would not re-run Lord Hutton's report.
"The issue of good faith was determined by the Hutton inquiry," he said.
The other members of the committee are: former chief of the defence staff Field Marshal Lord Inge; former senior civil servant Sir John Chilcot; Labour MP Ann Taylor, chairman of the Commons intelligence and security committee; and Conservative MP Michael Mates.
Foreign Secretary Jack Straw told MPs the committee would work in the same way as the Franks Inquiry into the 1982 Falklands war, which looked at how Britain failed to realise in advance that Argentina planned to invade the islands.
That means the committee will meet in private, but its findings will be published by the end of July, without revealing any sensitive intelligence material.
But Liberal Democrat Sir Menzies Campbell said his party could not accept the inquiry's remit and urged ministers to think again.
"Should not the prime minister and others in the special circumstances of this case be willing to submit to scrutiny of their competence and their judgement in the discharge of their responsibilities," he told MPs.
Conservative leader Michael Howard said changes he had suggested to the remit meant the inquiry would address the government's use of the intelligence, not just how it was gathered.
That would allow the public to judge for themselves whether the war was justified, he told BBC Radio 4's World At One.
Earlier, Mr Blair told the Commons liaison committee of the most senior backbenchers he had wanted consensus.
But he argued: "We can't end up having an inquiry into whether the war was right or wrong. That is something that we have got to decide. We are the politicians."
News of the inquiry follows the announcement of a US inquiry into its Iraq intelligence and Mr Straw said Lord Butler would work closely with the American commission.
President George Bush's creation of a bipartisan committee raised the pressure for a similar inquiry in the UK.
The intelligence used to send troops to Iraq is under scrutiny
Last week Downing Street said it would wait and see whether the Iraq Survey Group turned up evidence of WMD.
But Mr Blair denied US pressure had forced a change.
An inquiry was needed because it now appeared the Iraq Survey Group (ISG) could take months to produce its final report on the search for banned weapons in Iraq, he said.
And former ISG head David Kay had also said he thought there were not stockpiles of weapons of mass destruction.
'Defending the war'
Mr Blair stressed that Dr Kay had pointed to evidence of weapons of mass destruction "programmes".
If that was right, the legal basis for the war was "entirely secure", he continued.
He added: "I think we've done the right thing, not just because Iraq was a dangerous place under Saddam but also because the rest of the world needs to know that this issue will be tackled with firmness."
On Monday the Commons foreign affairs committee suggested that the "continued failure of the coalition to find weapons of mass destruction" had damaged UK and US credibility in their conduct of the war against terrorism.
Tuesday also saw Downing Street publish its response to the Commons intelligence and security committee's report on Iraq's weapons of mass destruction.
The committee had criticised the way the government presented its claim that Iraq could use some weapons of mass destruction within 45 minutes of an order, saying it allowed for speculation about its exact meaning.
Some newspapers suggested the weapons could be fired at British bases in Cyprus.
In its response, the government says it understands the committee's reasoning but "notes that the dossier did not say that Iraq could deliver chemical or biological weapons by ballistic missiles within 45 minutes".
And responding to a separate report by the Commons foreign affairs committee, it denied the claim had been given "undue prominence".
It adds: "The government stands by its interpretation in the dossier of the intelligence which was then available on the 45 minutes claim."