Mr Blair, in an interview, failed to condemn the controversial practice, which the British Government denied involvement in until only February this year, by saying: "The Obama government is going to continue [with them] in certain circumstances anyway."
In the July issue of Esquire, Mr Blair also spoke for the first time about the alleged torture of Binyam Mohamed, saying people should "wait for the facts" of his case.
In 2005, when details began to emerge of the rendition of terror suspects by the US to torture sites in East Africa and the Middle East, both Mr Blair and the then Foreign Secretary, Jack Straw, told the Commons that British airports had not been used and British forces played no part.
But in 2008, the Foreign Secretary, David Miliband, was forced to apologise to the Commons after admitting that US forces used the British overseas territory airbase in Diego Garcia for the "torture" flights.
And in February this year, John Hutton, the Secretary of State for Defence, finally admitted that Britain was involved in the rendition of two suspects, who were captured by SAS forces in Iraq and handed over to the US to be sent to Afghanistan.
"First of all, really wait for the facts. I didn't know about those things, incidentally. But my strong advice is: wait for the facts."
What Mr Hutton told the Commons in February "wasn't known by politicians", Mr Blair said, adding: "Look, we could go into a whole debate about renditions, and so on. I think you'll find that the Obama government is going to continue [with them] in certain circumstances anyway. It's only ever journalists who ask me questions about issues like that. It's not an issue [with people] out there."
Mr Hutton revealed that documents sent at the time to Mr Straw and the then Home Secretary, Charles Clarke, made reference to the rendition of the two terror suspects and admitted that more questions should have been asked.
Mr Mohamed, released from Guantanamo Bay this year, claims that he was tortured in Pakistan and Morocco and that his torturers were helped by MI5.
When Esquire attempted to clarify Mr Blair's remarks following the interview, a spokesman for the former prime minister said in a statement: "TB is, and always has been, opposed to torture, without qualification. He didn't want to get into a debate about the separate issue of rendition, because UK policy is clear, as is the Obama administration policy, and he didn't want to get into that debate between those two positions."
But the Conservative MP Andrew Tyrie, chairman of the all-party parliamentary group on rendition, who was last week in Washington meeting senior US legal advisers to discuss the issue, said Mr Blair's decision to "hide behind" President Obama was "ludicrous".
The MP for Chichester added: "If I hadn't watched Tony Blair in the Commons for so many years, I would be really shocked by his evasiveness on this. Blair, as ever, seems to want to be in two camps at once.
"Either you take the Bush/Cheney view that there are circumstances in which kidnap and torture are necessary in trying to prevent terrorism, or you take the view, as I do, that it is counterproductive: it is likely to damage the perception of the West in the eyes of those we are trying to persuade. It is ludicrous for Blair to hide behind Obama on this.
"Since Bush, there has been a fundamental change of policy in the US, which Blair must know, and Obama has inherited an extremely difficult situation, but he has made an unequivocal commitment to abandon torture.
"As for his pleas of ignorance, I'm speculating, but if our PM didn't know, given all the information that dribbled out in his six years as PM after 9/11, he must have gone out of his way to avoid asking awkward questions. To Obama's credit, he has had the courage to ask those questions."
In his interview, Mr Blair also risked irritating Gordon Brown by revealing he is not going to criticise David Cameron's government if the Tories win the next election. Backing the Prime Minister, he said: "Look, I support the Government and hope they win the next election and believe that they can. Of course they can. Should there at some point in time be a change in government I wouldn't go out and start attacking them, either... It's a really bloody hard thing, government, and the last thing you need is some elder statesman – in inverted commas – telling you what to do."
Mr Blair, asked whether being prime minister can "turn a man's head", said: "I'm probably the least qualified person to answer it. Erm, most people would say I haven't changed as a person much. Also, you do learn, and I certainly have learned, a lot of humility... And you realise you are very fallible, and that you make mistakes."
The former PM is tipped to become the EU's first full-time president if Ireland ratifies the Lisbon Treaty later this year, after two years as the international community's Middle East envoy.
Mr Blair denied that his role in the Middle East was "atonement" for the war in Iraq. He said he had not got very far in writing his autobiography, but added: "I want to do something different: [to explain] what it is actually like to be a normal person but with this responsibility; what sustains you."
He said he had made a "few friends in the life I've got now", adding: "Only friendships, you have to spend time on, that's difficult. I try to... I believe in friendship."
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