A day after world leaders joined two million people marching through Paris in support of peace and freedom of expression, key government and crossbench senators renewed demands that the government fulfil its abandoned pre-election promise to wind back protections in the Racial Discrimination Act.

The current law allows for the prosecution of people who espouse views that "offend, insult and humiliate" on racial and ethnic grounds – most notably conservative columnist Andrew Bolt, who was sued in 2011 by a group of light-skinned Aborigines for suggesting they were not genuine Aboriginal people.

On Monday, Liberal senator Cory Bernardi said the government had been "bullied" out of amending the act, while NSW crossbencher David Leyonhjelm said the Charlie Hebdo atrocity should be a "wake up call to anyone who thinks you can have a little bit of free speech".

He said preventing free speech through legal means and "Islamist pricks shooting journalists" were very different things but "two sides of the same coin" nonetheless.

In response to a public outcry led by ethnic groups, the government abandoned plans to amend Section 18C and 18D of the Racial Discrimination Act last year, saying it was more important to have the Muslim community on "Team Australia" and on side with tougher anti-terror laws.

Acting Prime Minister Warren Truss on Monday ruled out any renewed move to change the law.

"We should be bold and speak out about the things we want to speak out about but we can do that without changing section 18C. The government's come to a decision in relation to that issue and we're not proposing to change."

But the outpouring of sympathy for the staff of Charlie Hebdo will give new impetus to a private member's bill co-sponsored by Senator Leyonhjelm, crossbencher Bob Day, Senator Bernardi and his fellow Liberal Dean Smith which would largely effect the changes the government shied away from implementing.

The matter has once again split the Human Rights Commission, with Commissioner Tim Wilson, a Liberal appointee, backing Senator Bernardi's push.

"Now is the time for a sensible and constructive debate on how this [law] should be reformed to reverse restrictions on insulting and offensive speech," he told Fairfax Media.

"Charlie Hebdo could not have been published in Australia."

Mr Wilson has been travelling around the country hosting forums on free speech and said there was very little division between those who want race hate protections and those who favour unfettered freedom of speech.

But Race Discrimination Commissioner Tim Soutphommasane questioned whether a cartoon causing religious offence could be covered by the Racial Discrimination Act as Islam is not a race.

"If something racially offends someone they are free to make a complaint under the legislation but even then there is still free speech exemption under 18d [of the act] which protect artistic work or fair comment," he said.

"Free speech is a fundamental human right but it is not an absolute right."

The free market think tank, the Institute of Public Affairs, said on Tuesday that Charlie Hebdo could not exist in Australia.

"Leaders from around the world have united to defend the right of publications like Charlie Hebdo to publish content that is offensive to some," said Simon Breheny, director of the Legal Rights Project at the IPA.

"But a publication such as Charlie Hebdo would struggle to survive in Australia, due to laws that censor offensive, insulting, humiliating and intimidating speech.

"Section 18C could be used against the publishers of cartoons that satirise figures based on their race or ethnicity. Content not caught by section 18C would almost certainly be censored by current state religious vilification laws, which are specifically designed to target the kind of content published in Charlie Hebdo.

"The attack on Charlie Hebdo is an attack on freedom of expression. And as Prime Minister Tony Abbott rightly noted in response to this atrocity, 'freedom of expression is the cornerstone of a free society'.

"The Abbott government should seek to put the Prime Minister's words into action by repealing existing Australian laws that restrict free speech, starting with section 18C."

A number of migrant community leaders and Prime Minister Tony Abbott's adviser on indigenous affairs Warren Mundine called for no changes on Monday.

But Senator Bernardi said the government had been bullied into backing away from changes, saying "the time for being bullied is over – we cannot negotiate with the intolerant".

"Let's fight for fundamental freedoms and reject those who will pursue aims that are at odds with that," he said.

Opposition Leader Bill Shorten called on Senator Bernardi to stop using the Paris attacks to "justify divisive debates in Australia".

"I think it's distasteful and is pathetic that even before the dust is settled and families are still mourning their lost ones in Paris, that we see an Abbott government MP trying to turn the tragedy into a domestic political issue in Australia," he said.

"We haven't even had the funerals yet."

Renewed debate on the Racial Discrimination Act will be a headache for some Liberals in marginal seats with large migrant populations. Craig Laundy who holds the western Sydney seat of Reid on the slimmest of margins was forced to break ranks to oppose Attorney-General George Brandis' original plan as a result of immense pressure from within his electorate.

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