Senator Bernardi has moved the bill on behalf of several Government colleagues as well as crossbenchers including Pauline Hanson and Derryn Hinch.
The bill seeks to remove the words "offend" and "insult" from section 18C of the Racial Discrimination Act.
And, despite the Government and Labor saying they have no intention of changing the laws, some in parliament think the change may yet happen.
Prime Minister Malcolm Turnbull is facing an early test of his authority, with almost all Coalition backbench senators supporting the latest push to weaken the nation's race-hate laws.
Every Coalition backbench senator has signed on to the bill except Victorian senator Jane Hume.
The bill seeks to remove the words "insult" and "offend" from the Racial Discrimination Act, while still maintaining the more serious protections against hate speech.
Seven crossbenchers are also supporting the bill, including the bloc of One Nation senators and crossbenchers Derryn Hinch, Bob Day and David Leyonhjelm.
But Mr Turnbull says the Government has no intention of changing the law, saying there are more important issues.
"We have other, far more important priorities to deal with, the budget-repair agenda that I've spoken about earlier, the industrial-relations and workplace-reform agenda I've spoken about earlier. Now backbenchers are entitled to move -- seek to move -- private members' motions, as you know. There is a wide range of opinions in the community about section 18C and the language in it. But I can assure you, Mr Speaker -- I will just repeat what I said -- the Government has no plans to amend section 18C."
But 39 votes for the bill in the Senate would turn Cori Bernardi's bill into law.
And Derryn Hinch, the former media commentator, says he thinks it may be possible the changes will be supported by more than the current 27 senators behind it.
"18C is not dead. And, look, this isn't racial vilification. Look, I am as appalled and disgusted by racism and some of the things that are said by some of my opponents as anybody would be. If you believe in freedom of speech, you've got to accept the freedom of speech from ugly people as well. Yeah, the numbers are building, and I know that, in the lower house, there are a lot more Liberals who haven't come clean* yet. So, it's not dead by a long shot."**
Senator David Leyonhjelm also wants parliament to drop section 18C.
"The law does not require me to be offended. All it says -- and remembering that I am seeking to repeal this law -- all the law says is that it's reasonably likely to offend or insult somebody of that person or that group."
But Indigenous leader and Labor senator Pat Dodson has made an impassioned plea for the retention of race-hate speech laws.
Senator Dodson has called on Mr Turnbull to be unequivocal in opposing the changes and has urged him to get his side of parliament in order.
He says he is puzzled at attempts to change legislation that has been an important pillar of Australia's success as a multicultural nation.
The bill will have to go before the Scrutiny of Bills committee before it can be debated.
Senator Bernardi leaves next week for a three-month secondment to the United Nations, so it is unlikely the Senate will consider the bill before next year.
