The Morrison government is split on whether to support Labor’s call to amend discrimination law to prevent religious schools firing gay staff.

The Liberal deputy leader, Josh Frydenberg, and candidate for Wentworth Dave Sharma backed Labor’s call but Scott Morrison refused to commit to extend his promise to prevent discrimination against students.

On Monday Bill Shorten extended Labor’s offer to prevent religious schools expelling gay students by suggesting the government should also protect staff and teachers at risk of discrimination on the basis of gender or sexuality.

There has been widespread backlash against religious schools’ right to discriminate on the grounds of sexuality after a leak of the Ruddock religious freedom review revealed the panel recommended entrenching exemptions to discrimination law, albeit with safeguards.

Frydenberg told ABC Radio there would be negotiations on the legislation this week, but he didn’t think there should be any discrimination, and the current laws weren’t right.

“I don’t think there’s any room for discrimination, be it [against] a student or against a teacher,” he said.

“But that being said, we need to work through this process with the Labor party and ensure that we provide a bipartisan front to the country.

“I don’t think these laws are right. And I do think we need to ensure that there is no discrimination in either our workplaces or in our schools. That’s my feeling,” he said.

The Liberal candidate for Wentworth, Dave Sharma, opposed discrimination against both teachers and students at a candidates forum on Monday.

“I’m fundamentally opposed to discrimination in schools, for pupils or for teachers, on the basis of sexual orientation, gender, or really anything else for that matter,” he said.

“I believe that right should be removed to the extent that it exists in laws passed in 2013 by the previous Labor government.”

In question time, when asked about Frydenberg’s statement, Morrison said legal changes for students need to be “addressed urgently” in the current sitting fortnight but “there will be a time and a place” to address the issue of teachers after the release of the Ruddock report.

Earlier, in a statement Shorten said he was pleased that “both sides of politics are now united in the view that exemptions allowing religious schools to discriminate against children should be removed”.

“I believe we can use this goodwill to go further and remove the exemption that would allow a teacher or school staff member to be sacked or refused employment because of their sexual orientation.”

Shorten said as a father he tried “to teach my children to treat everyone with respect, and to view everyone as equal” and Australia’s laws should reflect “the values we teach our children”.

Labor senator Kimberley Kitching told Sky News that while discrimination on the grounds of sexuality is “unnecessary” schools can currently hire teachers who are “able to teach the ethos of the school”.

Kitching called for a “discussion” about removing discrimination law exemptions for teachers – but only after the release of the Ruddock review.

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 staff and students on the basis of sexual orientation, gender identity or relationship status.

In submissions to the Ruddock review many religious organisations, including the Catholic church, the Anglican archdiocese of Sydney, Christian Schools Australia and the Freedom for Faith group, called for a religious freedom act to give religious institutions a right to uphold their values in employment practices.

Earlier, Tony Abbott told 2GB Radio that he “absolutely” agrees that children should not be discriminated against but warned the government should be “a little bit cautious” with the reform to ensure that laws “designed as shields” did not “end up becoming swords”.

He cited high-profile cases against Bill Leak and the Queensland University of Technology under section 18C of the Racial Discrimination Act, which bans speech that offends, insults or humiliates people based on race.

The assistant minister to the deputy prime minister, Nationals MP Andrew Broad, has backed the right for schools to “be able to employ people that hold the values the parents expect”.

“If a parent sends their child to a school and they are paying for that school then they expect that school in their leadership, in their teaching faculty, to uphold the values that they believe in,” Broad said on Monday.

On Sunday the finance minister Mathias Cormann told ABC’s Insiders the Liberal party is united on the issue of protecting students, despite his cabinet colleague, Alex Hawke, saying religious schools should “absolutely” have the right to discriminate against LGBTI students.

“I don’t think it’s controversial in Australia that people expect religious schools to teach the practice of their faith and their religion,” Hawke told Sky News on Wednesday.

At a doorstop on Sunday, Morrison said he didn’t “foresee any problems” with changing the law with respect to students, saying he had “only had strong messages of support from my colleagues” since announcing the policy on Saturday.

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 schools’ ability to fire teachers if they married a person of the same sex.