Australia aims to ban private or religious schools from expelling students on the basis of their sexuality, Prime Minister Scott Morrison said on Saturday.

Debate over personal rights is growing ahead of a crucial by-election for Morrison's ruling Liberal-National coalition in the blue-ribbon Sydney seat of Wentworth on October 20.

"I will be taking action to ensure amendments are introduced as soon as practicable to make it clear that no student of a non-state school should be expelled on the basis of their sexuality," Morrison said in a statement.

The statement, which urged parliament to tackle the issue over the next two weeks, follows an offer of support by the largest opposition party, Labour, to repeal legal exemptions that allow religious schools to discriminate.

Archbishop Mark Coleridge, the president of the Australian Catholic Bishops Conference, called this week for equality in school employment and enrolment.

"Once employed or enrolled, people within a Catholic school community are expected to adhere to the school's mission and values," the Sydney Morning Herald newspaper quoted him as saying.

Australia's parliament voted to legalise same-sex marriage in December after a nationwide postal survey returned an overwhelming majority in favour of the unions.

Morrison said the government was working through its responses to the recommendations of a review panel to examine if the change to the law had restricted religious freedom. The recommendations have not been publicly disclosed.

"Our government does not support the expulsion of students from religious non-state schools on the basis of their sexuality," he added.