TONY Abbott's rejection of Liberal frontbencher Cory Bernardi's views that "Islam is the problem" because it is a totalitarian religion has failed to stop a growing debate within the party.

Mr Bernardi said he had received death threats after telling a radio station "Islam itself is the problem - it's not Muslims."

Frontbencher Kevin Andrews, the party's families spokesman, told The Sunday Telegraph he supported a debate over multiculturalism that balanced diversity with Australian values.

"What people want to see is that anyone here can speak English," he said. "That we don't see particular groups entrenched in particular locations.

"I don't see [Opposition immigration spokesperson Scott Morrison] pursuing an anti-Muslim migration line. He's just reflecting a feeling in the community."

Liberal Victorian senator Mitch Fifield yesterday also said immigrants needed to integrate with the community.

"Australians revel in diversity and embrace different cultures," he said, "but they expect people who come to Australia to sign up to mainstream values. You have to muck in with the rest of the community and not develop a sort of separate society.

"We need to heed the lessons of the UK where you have whole suburbs which are basically separate entities to the rest of the community.

"There are some interpretations of Islam which aren't healthy and aren't compatible with Australian values, such as sharia law."

Senator Bernardi said on Friday that multiculturalism had failed and many Australians had concerns about the isolation of Islam. But he was forced to clarify his remarks yesterday after Mr Abbott publicly rejected them.

Mr Bernardi waded into the debate to defend Mr Morrison in the face of Labor demands he resign for questioning the taxpayer cost of funerals for asylum seekers killed in the Christmas Island tragedy and then, reportedly urging shadow cabinet to exploit concerns about Muslim migration.

Mr Morrison, who was confronted by refugee protesters this week and publicly condemned as a racist, has passionately rejected suggestions he is anti-Muslim.

The leaks have sparked a hunt for the rat in Liberal ranks, with demands Mr Abbott read the riot act to Liberal MPs.

The Cook MP, who walked the Kokoda Track with Muslim children and Labor MP Jason Clare as a "healing exercise", has revealed that, far from his image as the Tin Man of politics, he agonises over the portfolio.

Colleagues have confirmed he wept when he learned of the Christmas Island tragedy.

"There are no easy moral choices in this debate," he said. . "Every person who has had this portfolio has wrestled with it. You carry it around with you all the time.

This is a difficult, morally vexing portfolio. The only reason you can get up every morning is because I think our policy is the right one. All I know is the only way I can stop kids going into detention is to stop kids getting on these boats."

Liberal MP Judith Troeth said she was concerned where the debate was headed and did not want to see a hardening of conservative issues "because we are a very broad church in the Liberal Party".

Originally published as Debate over Islam divides Liberal party