According to Sir Christopher Meyer, the former British Ambassador to Washington, who was at the dinner when Blair became the first foreign leader to visit America after 11 September, Blair told Bush he should not get distracted from the war on terror's initial goal - dealing with the Taliban and al-Qaeda in Afghanistan.
Bush, claims Meyer, replied by saying: 'I agree with you, Tony. We must deal with this first. But when we have dealt with Afghanistan, we must come back to Iraq.' Regime change was already US policy.
It was clear, Meyer says, 'that when we did come back to Iraq it wouldn't be to discuss smarter sanctions'. Elsewhere in his interview, Meyer says Blair always believed it was unlikely that Saddam would be removed from power or give up his weapons of mass destruction without a war.
Faced with this prospect of a further war, he adds, Blair 'said nothing to demur'.
Details of this extraordinary conversation will be published this week in a 25,000-word article on the path to war with Iraq in the May issue of the American magazine Vanity Fair. It provides new corroboration of the claims made last month in a book by Bush's former counter-terrorism chief, Richard Clarke, that Bush was 'obsessed' with Iraq as his principal target after 9/11.
But the implications for Blair may be still more explosive. The discussion implies that, even before the bombing of Afghanistan, Blair already knew that the US intended to attack Saddam next, although he continued to insist in public that 'no decisions had been taken' until almost the moment that the invasion began in March 2003. His critics are likely to seize on the report of the two leaders' exchange and demand to know when Blair resolved to provide the backing that Bush sought.
The Vanity Fair article will provide further ammunition in the shape of extracts from the private, contemporaneous diary kept by the former International Development Secretary, Clare Short, throughout the months leading up to the war. This reveals how, during the summer of 2002, when Blair and his closest advisers were mounting an intense diplomatic campaign to persuade Bush to agree to seek United Nations support over Iraq, and promising British support for military action in return, Blair apparently concealed his actions from his Cabinet.
For example, on 26 July Short wrote that she had raised her 'simmering worry about Iraq' in a meeting with Blair, asking him for a debate on Iraq in the next Cabinet meeting - the last before the summer recess. However, the diary went on, Blair replied that this was unnecessary because 'it would get hyped ... He said nothing [was] decided, and wouldn't be over summer.'
In fact, that week Blair's foreign policy adviser, Sir David Manning, was in Washington, meeting both Bush and his National Security Adviser, Condoleezza Rice, in order to press Blair's terms for military support, and Blair himself had written a personal memorandum to the President in which he set them out. Vanity Fair quotes a senior American official from Vice-President Dick Cheney's office who says he read the transcript of a telephone call between Blair and Bush a few days later.
'The way it read was that, come what may, Saddam was going to go; they said they were going forward, they were going to take out the regime, and they were doing the right thing. Blair did not need any convincing. There was no, "Come on, Tony, we've got to get you on board". I remember reading it and then thinking, "OK, now I know what we're going to be doing for the next year".'
Before the call, this official says, he had the impression that the probability of invasion was high, but still below 100 per cent. Afterwards, he says, 'it was a done deal'.