Prime Minister Malcolm Turnbull is facing an early test of his authority, with all the Coalition backbench senators supporting the latest push to water down the nation's race hate laws.

Key points: Cory Bernardi has the support from all but one backbench Coalition senator

Cory Bernardi has the support from all but one backbench Coalition senator Changing laws is not a priority for Malcolm Turnbull

Changing laws is not a priority for Malcolm Turnbull Conservative MPs believe the laws impede free speech

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Liberal Senator Cory Bernardi is expected to move a private member's bill on Thursday to remove the words "insult" and "offend" from the Racial Discrimination Act, while still maintaining the more serious protections against hate speech.

The ABC has obtained the Notice of Motion for the bill showing every Coalition backbench senator has signed on — with the exception of Victorian senator Jane Hume — as well as seven crossbenchers, including the bloc of One Nation senators and crossbenchers Derryn Hinch, Bob Day and David Leyonhjelm.

The ABC understands while Senator Hume has not co-sponsored the bill, she supports the amendments and will vote in favour of the bill.

Shadow Attorney-General Mark Dreyfus described the move as "an open rebellion" against Mr Turnbull and called on the Prime Minister to rule out any changes to the laws.

Mr Turnbull has previously said it was not a priority for his Government and Attorney-General George Brandis has released a statement saying the Coalition has no plans to change 18C.

Senator Bernardi denied he was deliberately undermining Mr Turnbull by pushing ahead with the changes, saying the issue could be dealt with alongside the other items on the Coalition's agenda.

But the re-emergence of the issue is a sign that Mr Turnbull faces as many challenges within his own party as he does in Parliament.

"Clearly governments, and all of us as parliamentarians, are capable of walking and chewing gum at the same time," Senator Bernardi told the ABC.

"The Government is entitled to set its own priorities but as am I, for my own constituency, and that's the Australian conservatives who want to see reform in this space.

"Now, I'm saying it's on the agenda."

He argued the controversial clause had been "misused" and said his push to amend the laws was the "right thing to do" and "absolutely consistent with Liberal Party philosophy".

"I think ultimately the Liberal Party, the Government will be very grateful they'll have the opportunity to reform 18C," he said.

The conservative senator acknowledged that he did not yet have enough support for the bill to pass but said he would work to convince his own party, and the Nick Xenophon Team, of the merits of amending the laws.

"We don't want to bring it to a vote until it's got its best prospects of getting through, and that means there's still some work to be done," he said.

"We still have to convince the Government that it's a good and worthy thing for it to do, particularly if it wants to re-connect with a base that seems a little disenfranchised at the moment."

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 7 minutes 54 seconds 7 m Liberal Senator Cory Bernardi joins Leigh Sales

Conservative MPs — still reeling from their party's disappointing election result — say the issue important to their base, arguing the laws, as they stand, impede free speech.

On Monday Nationals senator Barry O'Sullivan told the ABC the issue had been "hanging around like an old bag of veggie scraps" for the past 18 months and it was time to test its support in the Senate.

His Liberal colleague, senator Chris Back, acknowledged changing the laws was not the "highest priority" for the Government but said it was an important issue nonetheless.

"Intimidate, humiliate, vilify must remain in the legislation, but offend and insult is something, as I said to one of my Labor colleagues, you and I do across the chamber to each other all the time," he said.

When asked whether it was significant all the politicians backing the bill were white, Senator James Paterson said: "I don't think that someone's gender or their sexuality or their race or any other characteristic that defines them is a really relevant consideration on their policy perspectives".

Former prime minister Tony Abbott abandoned plans to soften the Racial Discrimination Act in 2014 after widespread criticism, particularly from ethnic groups.

But earlier this month, he lamented the fact that he did not push ahead with the plan and conceded his Government should have pursued a less ambitious change.

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