In an essay on his website, Blair, who led Britain into the Iraq war 11 years ago, argued instead that Iraq was in "mortal danger" as a result of the West's failure to act in Syria.
"It is inevitable that events… have led to a re-run of the arguments over the decision to remove (former Iraq president) Saddam Hussein in 2003," Blair wrote in the essay, published Saturday.
"But because some of the commentary has gone immediately to claim that but for that decision, Iraq would not be facing this challenge; or even more extraordinary, implying that but for the decision, the Middle East would be at peace right now; it is necessary that certain points are made forcefully."
He added that to properly understand the current situation – and to propose solutions - lessons had to be learned "not just" from the Iraq war, but also from subsequent Arab uprisings.
The comments by Blair, who is now a diplomatic envoy to the Middle East, come after fresh outbreaks of violence in Iraq over recent weeks.
But he argued: "(I)t is a bizarre reading of the cauldron that is the Middle East today, to claim that but for the removal of Saddam, we would not have a crisis."
Blair criticized the "sectarianism" of Iraq's current government – led by Prime Minister Nouri al-Maliki – which he said "snuffed out what was a genuine opportunity to build a cohesive Iraq."
An offensive led by the Islamic State of Iraq and al-Sham (Isis), a breakaway group from al-Qaeda, has made inroads into Iraqi Kurdistan, the autonomous region in the north of the country.
There were fears that the insurgents would soon approach the capital Baghdad, although Reuters reported Sunday that the offensive seemed to have slowed, following counter-attacks by government forces.
In the essay, Blair blamed the unrest in Iraq on events in Syria, where the insurgents were "trained and battle-hardened".
"(T)here is also no doubt that a major proximate cause of the takeover of Mosul by ISIS is the situation in Syria. To argue otherwise is wilful," he wrote.
He called on policymakers to set aside their differences and "act now".
"For three years we have watched Syria descend into the abyss and as it is going down, it is slowly but surely wrapping its cords around us pulling us down with it," he added.