Dodson baffled by hate speech push

Labor senator Pat Dodson can't understand why there's a fresh push to water down racial hate speech laws.

"People can say pretty much what they want to say these days," the indigenous leader says.

Senator Dodson and fellow indigenous Labor senator Malarndirri McCarthy pledged on Tuesday to sit down with their new crossbench colleagues for the good of the country - several of whom support changes to the racial discrimination act.

But they're prepared to step in if discussions are not held in a respectful way.

"We'll also be picking people up on things that are completely inappropriate in terms of race relations in this country," Senator McCarthy said.

Momentum is gathering inside the government for a change to section 18C, which makes it illegal to offend, insult, humiliate or intimidate someone because of their race.

Senior Liberals insist the government won't support the change but backbencher Cory Bernardi plans to introduce a bill in the first week of the new parliament that seeks to remove the words "offend" and "insult" from the act.

Former Queensland state MP turned federal Labor senator Murray Watt hopes to use his background as a lawyer with an interest in human rights to push the case for retaining 18C.

"I'm hoping to play a role in explaining why these sorts of protections are important," he told AAP.

One proponent of the change, Liberal James Paterson, conceded the government had more urgent priorities to deal with first.

But he remains hopeful of a vote on the matter within three years.

"I hope over time throughout our three-year term we can get to other more important matters like 18C," he told reporters as he arrived for senate school on Tuesday.

Senators Dodson and Paterson joined 14 newly elected senators for the first day of their three-day induction program at Parliament House in Canberra to learn the procedures of the upper house.

Both missed out on a proper induction having filled casual vacancies in the previous parliament.