But Labor leader Bill Shorten says the government's plan replaces one form of discrimination with another and has rejected the prime minister's proposal for a conscience vote of MPs.
The prime minister on Wednesday called on Labor to support his bill after the opposition and the coalition failed in the Senate to find a compromise on changing the Sex Discrimination Act.
The parties agree on the principle that schools should not be able to discriminate against LGBTI students, but have been unable to find a compromise.
"This is a good bill. It actually does what I think Australians would expect us to do - look after kids for who they are, but also ensure that in this country, religious freedom still means something," Morrison told reporters in Canberra.
The proposed laws eliminate schools' abilities to discriminate against students on the basis of their sexuality, gender or relationship status.
The Human Rights Commission and courts will also be required to take into account the religious nature of a school, and the best interests of the child, when deciding on a complaint.
Thirdly, a clause specifically allows religious schools to teach in accordance with their religious beliefs.
If Labor doesn't agree, Morrison says he is willing to have all MPs vote with according to their conscience.
"I'm offering it as a bipartisan deal on a conscience vote. I think members should vote their conscience on this," he said.
Shorten said the prime minister had sought to "weaponise" the debate, when there was bipartisan agreement on the principle.
"It's very disappointing the government in the lower house has chosen to put forward a proposal which will replace one form of discrimination with another," he told reporters.
"No one with a conscience supports discrimination."
Labor has advice that says the proposed changes go too far, especially the new clause allowing schools to teach "in good faith" their doctrines, tenets or beliefs.
"For example, a teacher or school could provide inferior instruction to a student on the basis of the student’s sex, sexual orientation, gender identity or intersex status or, indeed, exclude that student from instruction entirely," Mark Gibian SC said in advice to Labor.
"A teacher or school could, similarly, impose different or draconian instructional requirements on particular students for discriminatory reasons."