Scott Morrison has pledged that there are amendments to the discrimination laws to make it clear that no student at a private or religious school may be expelled on the basis of their sexuality.
In a statement after Labor's offer of dual support to establish the law that Morrison revealed, Attorney General Christian Porter will prepare amendments to legislation to close existing religious exemptions within weeks.
Meanwhile, the Greens have been trying to take advantage of the community's backlash against the right of religious schools to discriminate by asking large party leaders to legislate to protect gay teachers and other members of religious schools.
Morrison claimed that the recommendations of the Ruddock study on religious freedom – including a number of precautionary measures before children could be deported – had been reported incorrectly, creating "unnecessary confusion and fear for both parents and students".
"Our government does not support the expulsion of students from religious non-state schools based on their sexuality," he said. "I also know that this view is widely shared by religious schools and communities across the country."
Morrison said parliament could deal with the issue in "the next two weeks" with the promise of legislation that "will give all students and parents the certainty they need".
It remains unclear whether the new federal law will violate the laws in the majority of states that allow religious schools to discriminate, including New South Wales and Victoria, but by banning behavior at federal level, it is possible to Protect students without state laws changes.
On Thursday, Morrison changed his position to express fundamental opposition to discrimination against students on the basis of sexuality.
Shorten wrote Friday to Morrison and offers to help remove the exemptions that religious schools allow to discriminate against children based on their sexual orientation and gender identity.
He said that Labor is "ready" to have a further discussion about the Ruddock recommendations, but the Australians could not say anything until after the release of the report.
Labor's offer stops with his MPs to vote on the Greens law to withdraw all religious exemptions and the party has previously said that it has "no plans" to change the law to dismiss gay teachers to prevent.
Debate was unleashed on Wednesday by the leakage of recommendations from the Ruddock study into religious freedom, including the modification of the federal Sex Discrimination Act to provide "that religious schools may discriminate in relation to students on the basis of sexual orientation, gender identity or relationship status" .
The report included several safeguards, including making schools compulsory to show that discrimination is based on religious rules, and ensuring that any discriminatory policies are made public and that schools have to take the interests of the child into account as primary consideration.
Di Natale wrote Friday to both leaders in similar terms and welcomed their comments in opposition "to any school, religious or not, discriminating students for being LGBTIQ +".
"It's good to see that you finally show leadership on this issue and use your voice to protect vulnerable young Australians against discrimination and victimization," Di Natale wrote to Morrison.
"But I also ask you to use your position in parliament to soften this protection in legislation, for students but also for teachers in religious schools."
Di Natale said that the Greens will submit a bill for private members this week when the parliament resumes on Monday and calls for both the coalition and the labor to "oppose the greens against discrimination".
Di Natale told Guardian Australia that it was "not good enough" for Bill Shorten and the Labor Party to leave LGBTIQ teachers. "
"The reality is that if they would seriously treat this as something other than a political problem, they would work with us to approve our legislation, which has already been drafted and makes schools across Australia safer for LGBTIQ people of all ages. "
Rodney Croome, a spokesperson for the Just Equal LGBT lobby group, said since the Ruddock report leaked: "political leaders have criticized discrimination against LGBTI children at religious schools" but less attention has been paid to discrimination against LGBT teachers, administrative staff and parents.
"Teachers should be deployed on the basis of their skills, not their sexuality, to give students the best possible education," he said.
"We appeal to Scott Morrison, Bill Shorten … to condemn discrimination against hard-working teachers and to reverse laws that make this discrimination possible."
In 2017, Perth teacher Craig Campbell was fired from his job at a Baptist college after it became known that he was gay.
In May, a YouGov Galaxy poll, conducted for Just Equal, stated that 82% were opposed to the exceptions to the discrimination laws that allowed expulsion of gay and lesbian students and 79% opposed the school's ability to dismiss teachers as they marry a person of the same sex.