Labor's bill will change the Sexual Discrimination Act to prevent schools from discriminating against students on the basis of sexual orientation, gender identity or intersex status.
It is likely the legislation will act as a political wedge, forcing the government to introduce its own legislation to parliament in the next few days.
Attorney-General Christian Porter said on Tuesday the protections proposed by the coalition to uphold school rules were modest and necessary.
He said it was important to allow faith-based schools to maintain rules like compelling students to attend religious services.
"We think that's a very reasonable protection for religious schools and they consider that is very important to the way in which they conduct their affairs," he told ABC radio.
The Greens want to go further than Labor, and will try to amend the opposition's legislation to include discrimination against teachers and staff.
"Labor needs to join the Greens in protecting teachers now. Not next year, not after the next election. No ifs, no buts, no more delays. We need to pass these reforms now," Greens Senator Janet Rice said.
"We can't afford any further delay before removing discrimination. Schools should be discrimination-free zones for all people, regardless of whether they are are a student or a staff member."
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