Govt won't support hate-speech change

The coalition's second most senior figure in the Senate insists the government won't be supporting a move by one of its backbenchers to change race hate-speech laws.

Liberal senator Cory Bernardi has thrown down the gauntlet to his colleagues, vowing to use the first week of the new parliament to introduce a private bill that seeks to remove the words 'offend' and 'insult' from a contentious section of the Racial Discrimination Act.

The government's position was very clear, Finance Minister Mathias Cormann told ABC radio on Thursday: "We will not initiate or support any changes ... it's a debate we had two years ago."

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

Senator Bernardi co-sponsored a private bill in the previous parliament that sought to remove the words 'offend' and 'insult' from the act.

Coalition supporters of the change believe they are within one or two votes of securing a Senate majority on the issue.