The Morrison government is seeking to amend the Marriage Act as part of its religious discrimination act, the first time the act will have been amended since the legalisation of same-sex marriage following the postal survey in 2017.

On the first day of the 46th parliament, the Department of Prime Minister and Cabinet released a list of legislation proposed to be introduced in the winter/spring sitting period.

Included in the list is the religious discrimination bill, which the government said would “make it unlawful to discriminate against people on the ground of their religious belief or activity (including lack of religious belief) and establish the statutory office of the freedom of religion commissioner at the Australian Human Rights Commission”.

The legislation would amend a number of existing laws, according to the document, including “marriage law, charities law and … anti-discrimination legislation”.

Guardian Australia has sought comment from the attorney general’s office.

New legislation was first announced in the government’s response to the Philip Ruddock-led review on religious freedom, which reported to government last year but was not introduced into parliament prior to the election being called in April.

Among the changes to the Marriage Act, outlined in the government’s response at the time, were plans to make it clear that religious organisations such as Catholic schools would not be required to make their halls available for same-sex marriage ceremonies, nor would they be required to provide services for same-sex weddings.

At the time, the attorney general, Christian Porter, said the proposed religious discrimination legislation would “not necessarily be very contentious” because it would be similar to other anti-discrimination legislation.

While the legislation is planned, it doesn’t appear to be written yet. The prime minister, Scott Morrison, reportedly told colleagues he wants to consult with Labor on the proposed legislation, and backbenchers will be allowed to shape the legislation through workshops with Porter starting later this week.

Labor’s shadow home affairs minister, Kristina Keneally, said Labor was willing to work with the government on the legislation.

Due to earlier leaks about the contents of the Ruddock report, the government was facing pressure from Labor and LGBT groups to legislate to prevent LGBT students being kicked out of religious schools, or LGBT teachers from being fired from religious schools on the grounds of their sexuality or gender identity.

The government instead asked the Australian Law Reform Commission (ALRC) to determine how to balance the rights of non-discrimination of LGBT students and staff with religious schools’ right to “maintain conduct and teaching in accordance with their faith”.

The ALRC report isn’t due until April 2020.

But Morrison and Porter are facing pressure from within their own party to bring the report forward to deal with all religious discrimination issues now in the wake of Israel Folau’s contract being terminated by Rugby Australia over social media posts warning hell awaits gay people.

In the Senate on Tuesday night, the Liberal senator Concetta Fierravanti-Wells said the report deadline should be brought forward before any new law is passed.

“I believe that the recent election has reinforced not only the need for more immediate legislative action but also the need for a more amplified and comprehensive referral,” she said.

“Indeed, it remains open to the attorney general to augment the ALRC referral and request that it report this year and before a religious freedom act is tabled. It makes greater sense for the issue to be dealt with comprehensively, rather than in the current piecemeal approach.”

It was a “new dawn” on the issue, Fierravanti-Wells said, adding that a religious discrimination bill would be too defensive in nature, and she would push for a stand-alone religious freedom bill to enshrine religious protections.