The man who ran Iraq after the 2003 invasion, Paul Bremer, has insisted that President George W Bush approved plans to dismantle Iraq's army.
Mr Bremer says the White House knew of the army dismantling plan
Mr Bremer released a series of letters to the New York Times detailing the need to take "robust" action against the toppled regime of Saddam Hussein.
But in a book published on Tuesday, Mr Bush says the agreed policy was to keep Iraq's army intact.
The disbanding is now widely seen as a mistake that fuelled Iraq's insurgency.
This episode is another example of a falling-out among senior administration officials about policy in Iraq, says the BBC News website's world affairs correspondent, Paul Reynolds.
In this case, the decision to disband the Iraqi army immediately after the invasion is now seen as a factor that contributed to the insurgency and nobody is keen to take authorship of it, our correspondent adds.
In a letter dated 22 May 2003, Mr Bremer, the former head of the US-led civilian administration in Iraq, appears to propose the dismantling of the army to Mr Bush.
"We must make it clear to everyone that we mean business: that Saddam and the Baathists are finished," Mr Bremer wrote in the letter quoted in the New York Times.
"I will parallel this step [dismantling the Baath Party] with an even more robust measure dissolving Saddam's military and intelligence structures to emphasise that we mean business.
"We are seeing signs that the outlawed organisations are behind some of the street violence here."
The next day Mr Bush replies, according to a second letter published in the Times: "Your leadership is apparent. You have quickly made a positive and significant impact. You have my full support and confidence."
Mr Bremer provided the letters to the New York Times on Monday after reading extracts of Mr Bush's contribution to a new book.
"The policy was to keep the army intact; didn't happen," Mr Bush is quoted as saying in the book, Dead Certain: The Presidency of George Bush.
The book, by Robert Draper, is informed by six intimate conversations with the president.