An overwhelming majority of Australians oppose legalising speech that "offends, insults or humiliates" on the basis of race, according to a new Fairfax-Ipsos poll that underscores the political danger the Turnbull government faces in softening the nation's race-hate laws.

As the Senate prepares to vote on amendments to section 18C of the Racial Discrimination Act later this week, the poll of 1400 voters shows 78 per cent of Australians believe it should be unlawful to offend, insult or humiliate someone on the basis of their race or ethnicity.

The government has proposed removing these words from the act and instead making it unlawful to intimidate or harass someone on the basis of race.

The poll shows support for amending section 18C has increased by 10 percentage points since 2014, suggesting the high-profile Queensland University of Technology and Bill Leak cases have undermined support for the law.