Labor Leader Bill Shorten told AAP that the law needs to change.
"In my discussions with religious educators, it’s clear this is not an exemption that they use or want to use," he said.
"These laws are no longer appropriate, if indeed they ever were appropriate. It’s time our laws reflected the values we teach our children."
They Greens have confirmed they will introduce their own amendment to stop discrimination against both students and teachers on the basis of sexual or gender orientation, a move earlier flagged by leader Richard Di Natale.
"If you want the privilege of educating the next generation of young Australians, you don't have the right to discriminate, period," Senator Di Natale said.
Former prime minister Tony Abbott said he was mystified by the debate, saying there was no evidence gay kids had been discriminated against by religious schools.
"By all means let's protect people against discrimination," he told Sydney radio station 2GB.
"But let's be very careful that anti-discrimination laws designed as shields are not converted by activists into swords."
Prime Minister Scott Morrison has refused to commit to extending amendments to cover LGBT teachers, saying "there will be further opportunities to discuss broader questions".
"What I'm most concerned about now is that children are at risk of being expelled from schools," he said.
Law Council of Australia’s President-elect Arthur Moses SC said now would be a good time to review whether these changes should apply to teachers but not at the expense of prompt protections for students.
"I would not like to see that used as a wedge to get rid of the immediate issue to ensure our children aren’t subject to discrimination," Moses said.
Catholic Schools NSW CEO Dallas McInerney welcomed the changes to anti-discrimination laws.
However he said Catholic education had never sought the right to expel students or to dismiss or refuse to hire staff based on their sexuality.
“All that we expect is that, once employed or enrolled, people within a Catholic school community adhere to the school’s mission and values," McInerney said.