The Greens say the federal government's law changes to stop religious schools excluding LGBT students don't go far enough and should also protect teachers.
The party has confirmed it will introduce its 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.
LGBT rights activist and spokesperson for just.equal Rodney Croome has also called on the government and Labor to ban discrimination against LGBT students and teachers.
"If students in faith-based schools are to receive the best possible education, teachers must be employed on the basis of their skill, not their sexuality, Mr Croome said on Saturday morning.
But 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.
Labor's education spokeswoman Tanya Plibersek also declined to pledge support for extending the laws, saying the protection of children was "a first step" and the opposition would then listen and speak with schools about discrimination against LGBT staff.
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," Mr 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," Mr McInerney said.