A review into religious freedoms will be released alongside the federal government's response before the end of the year, the prime minister says.
Cabinet is yet to consider the review led by former Liberal minister Philip Ruddock and handed to the government in May.
It urges the government to amend the Racial Discrimination Act or create a new Religious Discrimination Act to protect people of faith from discrimination, Fairfax Media reported on Thursday.
"I'm not comfortable with discrimination against people's religious faith, against their gender, against their sexuality, against their race," Scott Morrison told 3AW radio on Thursday.
"What this report is about is ensuring people can't be discriminated against because of their religious beliefs."
Protection of religious beliefs already exists in almost every state and territory jurisdiction, except NSW and South Australia.
The review proposes laws be amended in those two states but rejects calls for a Religious Freedom Act, which would give greater rights to people to express their religious beliefs, Fairfax says.
Opposition Leader Bill Shorten says the government should release the report before voters hit the polls for the Wentworth by-election.
"If there is nothing nasty in the report just put it out," Mr Shorten told reporters in Brisbane on Thursday.
"Why are we having a debate which says that the human dignity of children could be further subject to exemptions against discrimination?"
Liberal MP and former Human Rights Commissioner Tim Wilson has cautiously given his support to the leaked recommendation, pending the release of the review.
"I think the government would be very wise in releasing its response with the report," he told the ABC.
"Because what we saw yesterday was obviously a very strong emotive story which caused a lot of anxiety for people."
The review also recommends strengthening the right of schools to reject gay staff and students, it was reported on Wednesday.
Mr Morrison says religious schools should be able to operate according to their beliefs, but argues the review calls for the interests of children be put first.
"It puts the protection and interests of the child at the centre, which is not what that law currently does," he said.
"It should be fine-tuned to protect the interests of the child and make that paramount in any consideration."
Independent senator Derryn Hinch will move a notice of motion in the Senate next Monday, calling for government funding to be stripped from private schools that discriminate against teachers or students on sexuality grounds.
President of the Australian Catholic Bishops Conference, Archbishop Mark Coleridge, said Catholic schools welcomed staff and students from all backgrounds.