Labor is lobbying the coalition government to back laws banning religious schools from discriminating against gay students, a prohibition that both parties support in principle.
Federal politicians will this week debate removing the legal right for faith-based schools to expel or deny enrolment to gay children.
Prime Minister Scott Morrison first proposed the idea during the recent Wentworth by-election, saying he wanted the matter dealt with by the end of this year.
However, negotiations between the major parties failed after the government insisted new provisions be introduced to allow religious schools to enforce rules such as compelling gay students to attend chapel.
"Religious schools should be able to set reasonable rules in relation to the conduct within their schools," Cabinet Minister Mathias Cormann told Sky News on Sunday.
With hopes for a bipartisan bill dashed, Labor has introduced its own legislation to prevent schools from excluding students on the basis of their sexual orientation or gender identity.
"I'm happy to have a discussion about how we ensure that we preserve the capacity of religious schools to teach the tenets of their faith," Labor Senator Penny Wong told the ABC.
"Nothing in the bill that is being proposed by the Labor Party stops that."
Senator Wong said the new laws could be in place before Christmas if Mr Morrison and his coalition colleagues back Labor's proposal.
"Why doesn't he just ask his people to vote and do what they said they'd do?"
Even though religious schools overwhelmingly say they don't want or need the power to discriminate against gay students, both parties have taken up the issue after it was raised in the religious freedom review conducted by former government minister Phillip Ruddock.
The Greens want to go further than Labor, and will try to amend the opposition's legislation to include discrimination against teachers and staff.
Parliament is entering its final sitting week before the long summer break.
