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Blair called for Bush to help him form an international coalition against Islamic terrorism that would go beyond simply retaliating against Osama Bin Laden and Al Qaeda.
The note, sent on September 12, 2001, was declassified as part of the Chilcot Inquiry report into the Iraq war and its causes, released after 7 years on Wednesday.
Blair calls in the note for "an agenda that puts onto a new footing action against this evil."
"If this is a war - and in practical, if not legal terms, it is - we need war methods," he writes.
He called for the West to take a hard line and crackdown on abuses of "laws that in a democratic society they abuse." Blair wrote: "The West has pussyfooted around with these issues. These groups don't play by liberal rules and we can't either."
Later in the note Blair says: "Some of this will require action that some will baulk at. But it is better to act now and explain and justify our actions than let the day be put off until some further, perhaps even worse catastrophe occurs."
The note references Afghanistan extensively but does not mention Iraq. However, the Chilcot Report concludes that 9/11 played a role in the Iraq invasion, with Blair suggesting regime change there just 3 months after the attack.
The wider Chilcot Report is a damning indictment of Tony Blair's decision to take the
Here's the full note from Blair to Bush: