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Conservative Liberal senators aren't backing down from their crusade to water down racial discrimination laws, saying freedom of speech is under threat.

15 Oct 2015 - 1:48 PM  UPDATED 15 Oct 2015 - 1:53 PM

Senators on Thursday began debating a private bill to remove the words "insult" and "offend" from section 18C of the Racial Discrimination Act.

The bill is being sponsored by crossbenchers Bob Day and David Leyonhjelm and Liberals Cory Bernardi and Dean Smith - all strong supporters of free speech.

Outspoken Liberal Ian Macdonald believes anyone should have the right to insult and offend him and whoever else they choose.

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"If offending and insulting becomes a criminal act in Australia then we have lost one of those very valuable icons that define the Australian people," he told parliament.

The bill is seen by some as an attempt to skirt around the government's decision to ditch its own plans to water down the laws following resistance from ethnic groups.

Senator Macdonald accused Greens senator Scott Ludlam and his "nasty little band" of GetUp activists of orchestrating an offensive email and phone campaign against him.

"It's just insults, which says more about the people who are not only sending them, but also organising them," he said.   

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Fellow Liberal Zed Seselja said it was near impossible to determine what offends and insults by a so-called "hurt-feelings" test.

"Outlawing speech doesn't stop the bigotry in people hearts," he said, while calling for racist comments to be brought out into the open and discredited.

Labor fiercely opposed the bill, calling on Prime Minister Malcolm Turnbull to "stare down the less tolerant parts of his party".

Senator Sue Lions used the experience of her 11-year-old Indigenous grand-daughter who she says is followed around local shops by their owners because she's Aboriginal.

"Now that is offensive," she said.

"Who wants to make that legal?"

Senator Lines also cited "disgraceful" emails sent to indigenous colleague Nova Peris "because of the colour of her skin".

"They use terms that I would not even repeat in this place because they're so offensive."

Debate on the bill was adjourned.