In a press conference in the Western Australian seat of Hasluck on Saturday, Prime Minister Scott Morrison said the religious discrimination amendment would be introduced for a second round if he gets another term.

Mr Morrison said he would introduce a standalone bill to deal with enshrining additional religious protections into law despite the bill failing to pass earlier this year, after a number of Coalition MPs crossed the floor.

Earlier in the week, he confirmed he had written to a number of religious groups to assure them it remained a priority to implement an unamended version of the bill, adding it had been a great "disappointment" it wasn't passed in February.

But changes to protect LGBTQIA+ students and teachers from being sacked or excluded due to their sexuality won't be introduced simultaneously unlike the earlier proposal.

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Mr Morrison said religious protections would be introduced first but didn't answer questions about when he would introduce the sex discrimination amendments, meaning religious institutions could expel students or fire staff on the basis of sexuality.

"I would like to see it happen," he said.

"Our commitment was for the [religious discrimination amendment] to go forward, and we will go forward with the [bill] in its own right."

When pressed by journalists for a timeline on how far apart the two bills could be introduced from each other, the Prime Minister declined to answer.

"Let's just wait until an election," Mr Morrison said.

"Let's just see what the Australian people decide."

The religious protections were one of Mr Morrison's key election promises during the 2019 campaign.

In February this year, the Coalition joined Labor and the Greens in agreeing not to debate the package in the Senate, following a marathon overnight sitting in the lower house.

A separate amendment to the Sex Discrimination Act to protect transgender students at religious schools from discrimination also passed, after five Liberal backbenchers joined Labor in backing Mayo independent MP Rebekha Sharkie's proposal.