Ministers have said they will hold an inquiry into the Iraq war as "soon as practically possible" after the bulk of UK troops leave in July.
The government has previously said it would only be prepared to contemplate an inquiry once the involvement of UK troops in combat operations ends.
UK troop numbers will be reduced from 4,100 to 400 by the end of July.
The Conservatives say there is no "reasonable impediment" to an immediate inquiry into the war and its aftermath.
Foreign secretary David Miliband said ministers were committed to holding a "comprehensive" inquiry but was not prepared to give any details of when this would happen.
Shadow foreign secretary William Hague told MPs that the process should begin straight away and it was a "grievous error" it had not already started.
The Lib Dems said the inquiry must be in public and its terms be wide-ranging to ensure it was not a "whitewash".
And the families of military personnel killed in Iraq have handed a letter into Downing Street calling for a full public inquiry.
Reg Keys, whose son was killed in Iraq in 2003, said he was "encouraged" that an inquiry would take place and by suggestions that it would be far-reaching.
Opposition parties and some Labour MPs have repeatedly called for an investigation into Iraq along the lines of the Franks inquiry conducted in the aftermath of the Falklands War.
With the bulk of UK troops set to leave within months and the security and political situation in Iraq "substantially improved", Mr Hague said it was "inconceivable" that an inquiry could not happen.
Shadow foreign secretary
The inquiry must look into how ministers "discharged their responsibilities" in the run-up to the war, Mr Hague said,
Other areas that must be examined included the use of intelligence, how the UK dealt with the US and other allies and why planning for post-war Iraq was so inadequate.
Mr Hague said opposition to an inquiry within the government had "evaporated" and many Labour MPs backed a move.
He expressed concerns ministers were contemplating a "more limited" inquiry than most MPs and the British public expected.
He also suggested that ministers may want to delay an inquiry for as long as possible so that its findings would not be published until after the next general election.
If Labour did not set up an inquiry, the Conservatives would do it as one of its "first acts" should it win the next election.
"We will learn the necessary lessons and what went wrong in the functioning of government itself," Mr Hague said.
Mr Miliband said the UK's "sole focus" was on ensuring a "smooth and effective conclusion" to the UK's combat operation in Iraq.
"The time to focus on an official inquiry is when the troops come home to safety, not when they are exposed to dangers in Iraq," he told MPs.
However, he said any inquiry would be "comprehensive" and look at the conduct of the war and its aftermath.
He said lessons could be learnt from an inquiry particularly with regard to post-conflict reconstruction and governance.
The Lib Dems said it would fight to ensure that the inquiry was not "narrow and secretive".
"To be effective this inquiry cannot sit in private and must be open and transparent as possible," said its foreign affairs spokesman Ed Davey.
"It must focus primarily on the political decisions - and failures - that led to this catastrophic war, rather than military ones."
Plaid Cymru said the inquiry should have been held "years ago".
"Labour plan to begin the inquiry after the end of the current parliamentary year when there is no-one to scrutinise it, start in in the autumn when everyone will be looking at the pre-budget report and release it quietly in the Spring, buried under the general election," said MP Adam Price.
The SNP said an inquiry was needed because the war was "based on the lie".
"It was the first time that the UK went to war on dodgy, unsound intelligence and I hope it is the last," said MP Angus MacNeil.
"The claim that Iraq had weapons of mass destruction that could reach us in 45 minutes was a big, whopping factual lie."
The war was the result of an "odd, sycophantic desire to appease the discredited former US President George Bush by Tony Blair", he said.
Two inquiries - the Hutton and Butler inquiries - have already been held into aspects of the Iraq war.
The Butler inquiry looked at intelligence failures before the war while the Hutton inquiry examined the circumstances leading to the death of former government adviser David Kelly.