The former prime minister is in the United States to participate in the Middle East peace talks. In the first direct talks in 20 months, Blair is representing the quartet that's involved in arbitrating a peace process between Israelis and Palestinians.
Blair expressed optimism about the peace process that has stalled numerous times, and praised President Obama for making it a priority right at the start of his presidency.
In his book, Blair writes that one of the biggest issues in solving that crisis is that no leader has gripped it for long enough or firmly enough.
The Bush administration "came to grip it, but it was late on in the presidency, and that's the important distinction with President Obama now," Blair told Amanpour. "I think you cannot overstate the importance of President Obama coming in and saying right from the beginning we're going to grip this, because that allows you, you see, to go through what will inevitably be the ups and downs."
Blair took considerable heat for supporting the 2003 U.S.-led invasion against Iraq, and becoming one of President George W. Bush's staunchest international allies.
Blair told Amanpour he feels an "enormous responsibility" for lives lost in Iraq. But he stood firmly by his decision to support Bush even though weapons of mass destruction were never found and the Iraq war led to a drain on resources in Afghanistan.
"You would be inhuman if you didn't regret the death of so many extraordinary, brave and committed soldiers, of civilians that have died in Iraq, or die still now in Afghanistan. And of course you feel an enormous responsibility for that, not just regret," Blair told "This Week's" Amanpour.
"But in the end, I believed and still do that if we left Saddam there, we would have had a different sort of problem, also with consequences and also with many people dying. So that's the difficulty for me, and likewise in Afghanistan," he added. "I think if we hadn't taken on the Taliban and hadn't taken on what had been a training ground for al Qaeda, we would be in trouble."
Hussein couldn't be contained, Blair argued, and even though it might have been better to focus on Afghanistan first, the former prime minister said world leaders couldn't take that risk.
Blair wouldn't rule out an attack against Iran if he was leading the country and was faced with the threat of Iran acquiring a nuclear weapon.
"I would tell them they can't have it, and if necessary, they will be confronted with stronger sanctions and diplomacy. But if that fails, I'm not taking any option off the table," he said.
"When you're a leader sitting in the hot seat having to take the decision, supposing your worst case materializes," and Iran acquires nuclear capability and then decides to use it, or share that technology with someone else, "Then what?"
Blair also defends former President Bill Clinton, who he dubs his political soul mate in the book.
"I think he was one of the first people really to understand, to articulate how progressive politics couldn't be a rainbow collation, that you had to stand up and be connected with people, not activists, simply," Blair told Amanpour. "And because in his concept of reinventing government, which he and Al Gore took forward, I think there's completely on the essence of the modern progressive politics."