Mr Abbott has called for a "religious revolution" inside Islam and declared: "Cultures are not all equal.
We should be ready to proclaim the clear superiority of our culture to one that justifies killing people in the name of God".
He initially made the comments in a Sky News interview, and backed them up in an opinion column published by News Corp. "We've got to work closely with live-and-let-live Muslims because there needs to be, as president Abdel Fattah Al-Sisi of Egypt has said, a religious revolution inside Islam," Mr Abbott said.
Speaking on ABC local radio, the Prime Minister said Mr Abbott was entitled to his personal opinion.
"It's a complex area," Mr Turnbull said.
"Plainly the vast, vast majority of Muslims are as appalled by extremism, and particularly violent extremism, as we are," Mr Turnbull said.