Speaking to an audience at the Library of Congress in Washington, Blair insisted that defeating the terror group on the ground is only the first step in tackling extremism, claiming the ideology itself must be eradicated.
On Wednesday evening British MPs voted overwhelmingly in favor of launching airstrikes against IS targets in Syria.
Mere hours after the vote, RAF Tornado jets carried out bombing raids on oilfields in the east of the country.
However, Blair cautioned that airstrikes are “only a necessary beginning.”
“For Europe, there is a huge calculation to be made. This security threat is at our door. It is actually within our home,” he said.
“We have a paramount interest in defeating it, which is why last night’s vote in the British House of Commons was so important.
“Europe has to create, within its nation states, the armed force capability to allow us not just to play our part, but to lead.”
Blair, who led the UK into the invasion of Iraq in 2003, said extremist ideology must be tackled in order to defeat IS. He claimed key aspects of IS ideology stretch “deep into parts of Muslim society.”
“A belief in innate hostility between Islam and the West is not the preserve of the few.
“Of course a large majority of Muslims completely reject Daesh (IS)-like jihadism and the terrorism which comes with it.
“However, in many Muslim countries large numbers also believe that the CIA or Jews were behind 9/11. Clerics who proclaim that non-believers and apostates must be killed or call for jihad against Jews have Twitter followings running into millions … The ideology has deep roots. We have to reach right the way down and uproot it.”