Scott Morrison has promised discrimination law amendments to make clear no student at a private or religious school should be expelled on the basis of their sexuality.

In a statement following Labor’s offer of bipartisan support to fix the law Morrison revealed attorney general Christian Porter will draft amendments for legislation to close existing religious exemptions within weeks.

Meanwhile, the Greens have sought to capitalise on community backlash against religious schools’ right to discriminate by calling on major party leaders to legislate to protect gay teachers and other staff of religious schools.

Morrison claimed the recommendations of the Ruddock religious freedom review – which included a number of safeguards before kids could be expelled – had been misreported creating “unnecessary confusion and anxiety for parents and students alike”.

“Our government does not support expulsion of students from religious non-state schools on the basis of 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 address the matter in “the next fortnight”, promising legislation that “will give all students and parents the certainty they require”.

It remains unclear if the new federal law will override laws in the majority of states that allow religious schools to discriminate, including New South Wales and Victoria, but by prohibiting the conduct at a federal level it may be possible to protect LGBT students without state law changes.

On Thursday Morrison reversed his position to express in-principle opposition to discrimination against students on the grounds of sexuality.

Shorten wrote to Morrison on Friday, offering to help remove the exemptions that allow religious schools to discriminate against children on the basis of their sexual orientation and gender identity.

As a father, I try and teach my kids to treat everyone with respect. I’ve written to the Prime Minister offering support to remove the current laws which allows discrimination against children because of who they are. It’s the right thing to do. pic.twitter.com/kleuyzkiV2 — Bill Shorten (@billshortenmp) October 12, 2018

He said Labor “stands ready” to have a further discussion about the Ruddock review recommendations but the Australian people could not have their say until the report was released.

Labor’s offer stops short of committing its MPs to vote for the Greens bill to repeal all religious exemptions and the party has previously said it has “no plans” to change the law to prevent firing of gay teachers.

Debate was sparked on Wednesday by the leak of recommendations from the Ruddock religious freedom review, including to amend 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 requiring schools to prove the discrimination is founded on religious precepts, ensuring any discriminatory policy is made publicly available and the schools must take into account the best interests of the child as the primary consideration.

Di Natale wrote to both leaders on Friday in similar terms, welcoming their comments in opposition “to any school, religious or not, discriminating against students for being LGBTIQ+”.

“It’s good to see you finally showing leadership on this issue and using your voice to protect vulnerable young Australians from discrimination and victimisation,” Di Natale wrote to Morrison.

“But I also ask that you use your position in the parliament to cement this protection in legislation, for students but also for teachers in religious schools.”

Di Natale said the Greens would introduce a private members bill this week when parliament resumes on Monday, and called on both the Coalition and Labor to “stand with the Greens against discrimination”.

Di Natale told Guardian Australia it was “not good enough for Bill Shorten and the Labor party to abandon LGBTIQ teachers”.

“The reality is that if they were serious about treating this as anything other than a political problem, they would work with us to pass our legislation, which is already drafted and which makes schools all across Australia safer for LGBTIQ people of all ages.”

Rodney Croome, a spokesman for the LGBT lobby group Just Equal, said since the Ruddock report was leaked “political leaders have decried discrimination against LGBTI kids in religious schools” but less attention had been paid to discrimination against LGBT teachers, administration staff and parents.

“Teachers must be employed on the basis of their skill, not their sexuality, if students are to receive the best possible education,” he said.

“We call on Scott Morrison, Bill Shorten … to condemn discrimination against hard-working teachers and roll back laws that allow this discrimination.”

In 2017 Perth teacher Craig Campbell was sacked from his job at a Baptist college after it became known he was gay.

In May a YouGov Galaxy poll, conducted for Just Equal, found 82% opposed the discrimination law exemptions that allowed expulsion of gay and lesbian students and 79% opposed the schools’ ability to fire teachers if they married a person of the same sex.