Mr Turnbull has extended an olive branch to the Liberal Party's right-wingers by publicly endorsing a milder proposal to reform Section 18C of the act, which conservative commentator Andrew Bolt was found to have contravened in 2011.

Mr Turnbull made the comments during his first ever appearance on Bolt's television program. The two have spectacularly clashed over the years on issues like same sex marriage, climate change and the Liberal leadership, with Bolt criticising the former leader for being too left wing. The party's right wing was instrumental in ousting Mr Turnbull from the leadership of the party in 2009 over emissions trading.

Family First senator Bob Day put forward a compromise proposal after Prime Minister Tony Abbott reneged on his election promise to repeal the act.

The Day amendment would strike out the words "insult" and "offend", meaning it would no longer be an offence to insult and offend a person on the grounds of race. It would, however, remain an offence to intimidate or humiliate a person.

Mr Turnbull said he was "very comfortable" with the so-called Day amendment and did not believe it would have "any negative impact". But he stressed the government's policy is to leave Section 18C unchanged.

The minister said the government's attempt to overhaul the act "ran off the rails" because the original proposal went "much further" than previously signalled and produced a backlash.

"I think the government went further than it should have. The reality is with change like this you've got to do it very delicately and you've got to bring people along with you," Mr Turnbull told Network Ten.

Up to half a dozen Liberal senators have previously told Fairfax they are willing to cross the floor to support the Day amendment, which is being co-sponsored by Liberal Democrat senator David Leyonhjlelm and two Liberals: Dean Smith and Cory Bernardi.

Senators Smith and Bernardi welcomed Mr Turnbull's endorsement and called on Prime Minister Tony Abbott to reopen the debate, saying the government now had political capital to re-prosecute the case for free speech.

Senator Bernardi said Mr Turnbull's support for the Day amendment reflected the Australian majority and "mainstream values."

"The government needs to reconsider its position on 18C to rebuild faith with those who believe in free speech," Senator Bernardi said.

"The recent budget has proved a change in approach can be very well received," he said.

Senator Dean Smith said changing 18C would "take time" but "will happen".

"Proponents of reform are prepared to be patient because international events are working to reinforce the case for reform not against it," Senator Smith said.

"The government's improving electoral stocks is an opportunity for important debates of principle to be resurrected," he said.

And Senator Smith also took a shot at Attorney-General George Brandis' development of the original policy.

"The execution of the original debate around section 18c was a low point in the government's policy development and salesmanship," he said.

Bolt breached the act in a series of articles in which he claimed prominent Aborigines had identified as Indigenous for professional advantage.

The Opposition's spokeswoman for Multiculturalism Michelle Rowland accused Mr Turnbull of wanting to weaken protections against "racist hate speech" "in an attempt to win favour with the right wing of the Liberal party".

"Malcolm Turnbull's comments show that no matter who is leading the Liberal Party, it cannot be trusted to preserve the protections against racist hate speech," Ms Rowland said.

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