Mr Turnbull says glib one-liners like Mr Abbott's could play into the hands of terrorists.
Treasurer Scott Morrison told Sky News Mr Abbott himself once advised him that politicians should not dabble in theology.
Greens leader Richard Di Natale told Sky News Mr Abbott was an embarrassment on the world stage.
'He's an incredibly divisive, destructive force within the Australian political landscape
'The sooner Tony Abbott disappears from the Australian political scene, the better for him, the better for the Australian community,' Senator Di Natale said.
Labor MP Ed Husic said politicians need to think carefully before making potentially divisive comments about one part of the population.
'What they are saying to the public is that if you are of the Islamic faith, you are being hard-coded against Western values, which is garbage,' Mr Husic told Sky News.
Opposition Leader Bill Shorten labelled Mr Abbott's comments counterproductive and called on Malcolm Turnbull to 'pull Tony Abbott into line'.
'Inflammatory language undermines efforts to build social cohesion, mutual respect and has the potential to harm the efforts of national security agencies to keep Australians safe,' Mr Shorten said in a statement.
The former prime minister also urged Australians not to apologise for holding Western values, calling for a 'restoration of self confidence' in the West.
'All cultures are not equal, a culture that believes in decency and tolerance is much preferred to one that says you can kill in the name of God,' he said.
Writing in News Corp papers on Wednesday, Mr Abbott took a similar line, calling for a 'hearts and minds' campaign against extremist views within the Islamic faith.
'There also needs to be a concerted hearts and minds campaign against the versions of Islam that make excuses for terrorists,' he said.
Speaking with Sky News' Paul Murray, Mr Abbott also took a hardline tone on national security and was quick to point out US President Barack Obama's reference to Islamic State as a death cult during his Oval Office address on Monday.
Mr Abbott said Islamic State cannot been contained , but must be destroyed, and to do so will require a 'strong security response' and a 'hearts and minds response'.
The former prime minister opened up about his plans for his future in politics, indicating he won't shy away from speaking out when necessary.
