Tony Abbott has accused the nation’s spy chief of tiptoeing around the subject of Islam and terrorism.

The former prime minister says Australia can’t pretend there isn’t a problem with Islamic extremists and called on moderate Muslim leaders to do more to denounce attacks.

“We keep tiptoeing around this subject,” Mr Abbott told 2GB’s Ray Hadley on Monday.

“The problem is that nearly all of the terrorist incidents are associated with people shouting out ‘Allahu akbar’ as they kill.”

Mr Abbott was responding to the comments of ASIO chief Duncan Lewis who told a Senate hearing last week had no evidence to suggest any connection between refugees and terrorism.

“We are not interested in religion – we are interested in whether an individual is exhibiting or expressing violence,” Mr Lewis told One Nation leader Pauline Hanson who advocates a ban on Muslim refugees.

Mr Abbott said ASIO had to have good relationships with the Islamic community in order to obtain information from them.

But it also had to command the confidence of the whole Australian community and be open and upfront about the issue.

“You can’t pretend that we don’t have a problem, that there isn’t a strain of Islam which is doing enormous damage to the whole world,” he said.

The overwhelming majority of Muslims around the world were decent people, but there was “this strain of ‘death to the infidel’ in Islam”.

“That’s why it’s vital that we work with ‘live and let live’ Muslims to try and ensure that this ‘death to the infidel’ strain is gradually massaged away,” Mr Abbott said.

“Every time there’s an incident, the same message has to be repeated. Any suggestion of ‘death to the infidel’ has no place in any modern religion.”