Anthony Albanese says his government remains open to amendments to push the draft bill through when MPs and senators meet in Canberra on Monday.
"The parties of government should be supporting this across the board," he told reporters in Brisbane on Friday.
The bill is the government's response to the Islamic-inspired terror attack that claimed 15 lives at a Bondi Beach Hanukkah event on December 14.
Opposition Leader Sussan Ley for weeks demanded Labor recall parliament before Christmas to adopt Australia's envoy to combat anti-Semitism Jilian Segal's report, which included proposed anti-vilification laws.
That's prompted the prime minister to call on the opposition to suggest changes.
"At the moment this is like trying to grab smoke, trying to get an arrangement with the coalition," Mr Albanese said.
"I say to the coalition, if you can let me know now what they are prepared to vote for, I will respond to any question people have, because at the moment I am not sure what it is, and I don't think they know either."
The coalition and the Greens oppose the draft bill in its current form, with Ms Ley describing it as "pretty unsalvageable" and Greens leader Larissa Waters wanting it expanded to protect other marginalised communities, including disabled, LGBTQ and other religious groups.
The support of either party is required to pass the legislation through the Senate.
A group of independent MPs, including Allegra Spender, whose electorate includes Bondi Beach, urged parliament to work across party lines to pass the laws.
"We urge all MPs to negotiate in good faith to deliver concrete action. We can't afford to wait any longer," the MPs, including Monique Ryan and Zali Steggall, said in the joint statement.
Ms Ley said the coalition was not consulted in the bill's design, but Mr Albanese said he had met with the opposition leader weekly.Â
She has voiced concern the bill is rushed and falls short of eradicating anti-Semitism and Islamic extremists.
A broad range of legal experts, Jewish groups and religious leaders have also criticised the bill, claiming it is too rushed and broad although the Executive Council of Australian Jewry has called on the coalition to vote in favour of the legislation.
In a submission to the parliamentary inquiry scrutinising the changes, the Australia Israel and Jewish Affairs Council said it would support a "short delay" in the bill's passage for further review and refinement.
The group recommends splitting the parts of the bill dealing with firearms into separate pieces of legislation to ensure disagreements over gun reform do not hinder the passage of new hate speech laws.
The bill includes measures such as cracking down on hate preachers, introducing hate speech and racial vilification offences, in addition to creating a national gun buyback scheme.
The Nationals have indicated their opposition to gun reform on behalf of farmers.
Coalition members will meet virtually on Friday afternoon to discuss concerns held over the bill and provide feedback on the position that should be taken.
Labor senator Raff Ciccone, the chair of the Parliamentary Joint Committee on Intelligence and Security, is drafting the report as he attempts to maintain the tradition of the group's bipartisanship.
A Labor caucus meeting will be held on Monday morning.
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