In an interview on United States television, Mr Blair has apologised for mistakes made in planning the war, but he says he does not regret bringing down Saddam Hussein.
Former British prime minister Tony Blair has apologised for supporting the United States-led invasion of Iraq with intelligence that turned out to be wrong.
Ahead of the invasion, the US, British and Australian leaders based their case partly on intelligence they said pointed to Iraq having weapons of mass destruction.
The Western powers later found none after driving Iraqi president Saddam Hussein out of power.
Tony Blair has now apologised for relying on the false intelligence and for what he calls "planning mistakes".
"I can also apologise, by the way, for some of the mistakes in planning and, certainly, our mistake in our understanding of what would happen once you removed the regime. But I find it hard to apologise for removing Saddam. I think, even from today in 2015, it is better that he's not there than that he is there.
Mr Blair says there are elements of truth, though, in the view that the invasion played a part in the rise of the self-proclaimed Islamic State, or IS, also known as ISIS.
"Of course, you can't say that those of us who removed Saddam in 2003 bear no responsibility for the situation in 2015. But it's important, also, to realise, one, that the Arab Spring which began in 2011 would also have had its impact on Iraq today, and, two, ISIS actually came to prominence from a base in Syria and not in Iraq."
Mr Blair pointed to conflicts in other countries to argue the policy debate on Western intervention remains inconclusive.
"We have tried intervention and putting down troops in Iraq. We've tried intervention without putting in troops in Libya. And we've tried no intervention at all but demanding regime change in Syria. It's not clear to me that, even if our policy did not work, subsequent policies have worked better."
On the streets of Baghdad, many Iraqis have criticised the allied intervention in their country.
Some say they are glad Saddam Hussein was removed from power, but even they criticise Britain and its allies for the deterioration in Iraq's security situation after his fall.
Civil activist Ali Al-Mandalawi is one.
"Saddam Hussein's regime was bloody to the Iraqi people, and toppling it was a favour. But after that, what did they (the British) offer? A lot of chaos and more destruction. We didn't see a real intention to build the state. We didn't see a beneficial cooperation from the British side to the Iraqi people."
Ahmed Taher says Mr Blair's apology should have come years ago.
"Toppling the former regime, that's right. But after that, they -- the British -- didn't make decisions that serve the people. They made it easy for other countries, whether Western or Arab countries, to interfere in Iraq and its politics. So this apology came really late."
Mr Blair's decision to send troops to back the US-led invasion is still a live political issue in Britain, where a six-year public inquiry into the conflict is yet to publish its findings.
The leader of Britain's Labour Party, Jeremy Corbyn, says he believes the conflict was illegal.
He maintains Tony Blair should be tried for war crimes if it is shown he broke international law.
