The former prime minister has called for a "hearts and minds" campaign against extremist views within the Islamic faith, saying it needed religious revolution.
"We can't remain in denial about the massive problem within Islam," he wrote in News Corp publications on Wednesday.
"Islam needs to delegitimise the urge to behead all those who insult the Prophet - but only Muslims can do this."
Islam never had its own version of a much-needed reformation or enlightenment period.
"Fortunately there are numerous Muslim leaders who think their faith needs to modernise from the kill-or-be-killed milieu of the Prophet Mohammed."
Mr Abbott said some British and French Muslims felt sympathy for Islamic State, and he decried the "self-excusing rubbish" of local leaders who blamed the extremist group's rise on Western foreign policy.
Australians should stop being apologetic for values which have made their country free, fair and prosperous, because some cultures were not equal.
"We should be ready to proclaim the clear superiority of our culture to one that justifies killing people in the name of God."
Mr Abbott is the most high-profile Liberal to urge for a debate on Islam and terrorism, joining cabinet minister Josh Frydenberg and other MPs who've made similar calls.
Liberal backbencher Angus Taylor said Mr Abbott had made an important point about the battle of ideas.
"The lack of self belief in the West has been a major issue in winning that battle," he told Sky News.
Colleague Craig Kelly said terrorist acts were being committed under a perverted interpretation of Islam and sweeping the issue under the carpet wasn't good enough.
But Labor frontbencher Ed Husic pleaded for social cohesion, begging conservative politicians to think carefully about their words.
Many Australian Muslims were with the broader community as defenders of its values and freedoms.
"We are as one to work against those who want to tear at those liberties," the Muslim MP said.
"Please ... let's do this in a way we lock arms to achieve this rather than pushing people away."
Australian Greens leader Richard Di Natale said Mr Abbott was a "very divisive force" and he did not speak for most Australians.
"Tony Abbott should pull his head in," he told Sky News from Paris.
Mr Abbott is set to deliver a similar call in a speech in Singapore where he is expected to urge for greater military efforts in the fight against Islamic State.
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