The federal government will consider stronger legal protections for religious groups, people with a disability and LGBTQ+ Australians after new hate speech laws drafted in the wake of the Bondi beach shootings pass parliament.

Parliament will sit on Monday and Tuesday next week to debate a bill which includes new hate speech and anti-vilification laws, powers to formally designate groups as proscribed organisations and provisions for the largest gun buyback scheme since the 1996 Port Arthur massacre.

The laws, set to be rushed through after a hasty parliamentary inquiry this week, have prompted calls for wider laws to ban the promotion and incitement of hatred, in addition to speech that threatens minority groups.

The legislation being debated next week is expected to give protections against antisemitic rhetoric targeting Australian Jews, as well as other race groups including the Sikh community.

Asked about other new hate laws on Tuesday, the prime minister, Anthony Albanese, said he expected more work going forward.

“On broader issues, what we intend to do is to have a process to look at other areas of hate speech. If the legislation is carried by the parliament, that will be referred to a process going forward,” he said.

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The health minister, Mark Butler, has also flagged protections for other characteristics including disability, gender and sexuality.

The independent MP Allegra Spender, whose electorate of Wentworth takes in Bondi beach and includes a large LGBTQ+ population, has called for wider hate speech protections.

She plans to move amendments to extend the current bill.

“I am pleased the government is considering further reform but disappointed their proposals are confined to race,” she said.

“As we know, hate takes many forms and to their great credit Jewish community leaders support inclusive laws to protect everyone.”

Equality Australia legal director, Heather Corkhill, said LGBTQ+ people should have protections under the new bill.

“We are seeing alarming and deliberate attacks against LGBTIQ+ people. The threats to our community are real and severe, and the need for stronger protections from hate and vilification has never been more urgent,” she said.

Officials from the attorney general’s department told parliament the legislation currently being considered was based on provisions from the Racial Discrimination Act, and was expected to extend protections to members of ethno-religious groups.

“We’re satisfied that that reference to persons or groups distinguished by race, colour or national or ethnic origin encompasses Jewish people,” deputy secretary Sarah Chidgey said.

Asked if Catholics, Christians or other religious groups would be protected, Chidgey said being Catholic alone would not be sufficient, though particular groups within wider religions might have the relevant characteristics.

It comes as several Coalition MPs pushed back on the bill, including Nationals MPs Matt Canavan and Bridget McKenzie.

Canavan said he would not support the plan, calling it “undemocratic, unconstitutional and so vague that they could easily be used to unjustly silence legitimate criticism of government policy”.

But the Labor senator Raff Ciccone urged MPs not to play politics with the bill, noting it had support from the Jewish community.

“Unfortunately, there are politics being played out, not because of this bill, but because of their own other internal politics,” he said.

“At the end of the day, we all need to work together and come together to stamp out antisemitism. That is what we have been tasked to do.”

In a statement, the minister for multicultural affairs, Anne Aly, said the government would consider more work once the current bill becomes law.

“No one in Australia should be subjected to any type of hate,” she said.

“Once the combating antisemitism, hate and extremism bill passes through parliament, the government is open to considering extending the protections to other types of hate.”

Albanese said he expected debate to wrap up by next Tuesday night.