Labor's move to ditch objectionable elements of the legislation - rushed in response to the Bondi terror attack - put the onus on the opposition to approve changes its own leaders called for, Finance Minister Katy Gallagher said on Sunday.
A day earlier, Prime Minister Anthony Albanese announced the government would split its original omnibus bill, which also included a planned gun buyback scheme, after the Greens signalled they would only support the firearms proposal.
The government now hopes to pass both bills by the end of Tuesday, but it will require the support of either the minor left-wing party or the opposition to get the measures through the Senate.
The most contentious element - a widely criticised offence against racial vilification - was also removed from the hate speech bill.
The Executive Council of Australian Jewry said it was disappointed at the removal of the vilification offence, arguing it sent a message that "deliberate promotion of racial hatred is not considered serious enough to be criminalised".
"We exhort the major parties to work together to get legislation passed now that will advance us further down the road towards having effective laws against the deliberate promotion of racial hatred," co-chief executive Peter Wertheim said.
But despite Labor's backdown, the coalition has yet to lend its support to the hate speech measures, which would strengthen penalties against people who threaten violence against protected groups and ban Islamic extremist organisations like Hizb ut-Tahrir and neo-Nazi group the National Socialist Network.
"It's time for action," Senator Gallagher told reporters in Canberra.
"These are really important responses to what we saw happen in Bondi. There is no reason to delay them. We've taken out the bit that people were concerned about.
"We now need to press forward on the areas where the opposition have been calling for this, calling for parliament to be recalled, calling for legislation of this nature."
Opposition Leader Sussan Ley previously labelled the omnibus bill "unsalvageable" as the hate speech element did not explicitly criminalise phrases such as "globalise the Intifada".
The opposition has also complained that the prime minister did not provide it with an opportunity to have input into the design of the legislation.Â
But following the announcement that the bill would be split, senior figures from Mr Albanese's office approached the opposition offering to work together and further amend the proposed laws to get them over the line, Liberal sources said.
Even before the coalition formalised an official position on the reworked hate speech bill, renegade Liberal backbencher Andrew Hastie was declaring his opposition to it on social media.
"When I look at the bill that's going to be debated in parliament next week, I ask the question: will this stop a future Bondi attack?" he said in an Instagram post on Saturday.
"I can't see an urgent capability gap that needs to be addressed in the AFP, ASIO or any other Commonwealth agency responsible for counter-terrorism. So the question is: why the rush now?"
Legal experts, Jewish groups and influential religious leaders also criticised the bill as too rushed and broad.
The Greens are opposed to the hate speech bill due to concerns it would limit the freedom of people to protest Israel's war in Gaza, but the minor party will support the gun laws.
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