The ideology of Islamic State has "deep roots" and support for its propaganda runs "deep into parts of Muslim societies", Tony Blair claimed yesterday.

Speaking at the Library of Congress in Washington, the former primer minister said, "Of course a large majority of Muslims completely reject Daesh-like [ISIS-like] jihadism and the terrorism which comes with it".

However, he also insisted that there is a widespread belief in "an innate hostility between Islam and the West".

"Those who believe in concepts of the caliphate and the apocalypse – so much part of Daesh propaganda – stretch deep into parts of Muslim societies... In many Muslim countries large numbers also believe that the CIA or Jews were behind 9/11," he added.

"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."

Blair praised British MPs for voting in support of air strikes in Syria on Wednesday and warned that without immediate action there may be "terrorist attacks potentially worse than those in Paris".

"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."

However, he urged the UK to adopt a holistic approach – a suggestion also made by Archbishop of Canterbury Justin Welby ahead of Wednesday's vote.

"Force alone will not prevail," Blair said. "The Islamist ideology has also to be confronted."