Federal Lyons MP Brian Mitchell will write to the Council for the Order of Australia about rescinding Bettina Arndt's Australia Day honours.
Ms Arndt, who is a conservative social commentator, became a general member of the Order of Australia earlier this year for services to gender equality.
She had previously come under fire for conducting a sympathetic interview with a convicted Tasmanian paedophile, but is facing renewed criticism over comments she made on social media following the murder of a mother and her three children in Queensland last week.
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Hannah Clarke and her three children were allegedly set on fire by her estranged husband while on the way to school on Thursday.
In the wake of the incident a Queensland police officer commented suggesting there was a need to investigate whether the man was driven to the act.
Ms Arndt praised the police for the comments.
Queensland police later apologised for the comments.
Mr Mitchell said her comments following the "tragic event" added to the evidence supporting the case for her Australia Day honours to be rescinded.
"You're between the devil and the deep blue sea, do you ignore what she says in order to not feed the beast or do you have to call her out?," he said.
He said it wasn't a political issue and that Ms Arndt was just fundamentally unfit to receive the award.
"Even without the controversy what has she done to deserve such an honour?" Mr Mitchell said.
"There are no two sides in this, there is no driving someone into that sort of act.
"The only person who is responsible for that terrible crime is the person who perpetrated it."
Ms Arndt said on Twitter 'feminist politicians' who criticised the initial police response to the murders was part of the problem.
She urged people to write to the police and politicians outlining their support for the police response.
Feminist politicians are now also piling on the Queensland police. It’s time for good, sensible people to step up. Write to your MP and the police supporting their measured and appropriate response. The police are right. The feminists are part of the problem, not the solution.— Bettina Arndt (@thebettinaarndt) February 20, 2020
Journalist Ginger Gorman, who is an expert in cyberhate, hatred expressed via a computer, and author of the book Troll Hunting, said Ms Arndt is behaving in the same way a predator troll would.
She said a predator troll is someone who uses the internet to do real life harm.
"I described Bettina as a predator troll because she only [follows] 47 [people on twitter]," she said.
"She's not on [Twitter] to engage but to broadcast."
What predator trolls do is latch onto emotive news stories & make outrageous commentary, bc they love the subsequent outrage and attention it brings them.— Ginger Gorman 🌈 (@GingerGorman) February 21, 2020
This is same behaviour.
A woman & her kids were burned to death by a violent man 😭 That’s the story. RIP. https://t.co/jWBISQIP3e
She said predator trolls try to create outrage by latching onto emotive news stories.
"What predator trolls do is latch onto emotive news stories and make outrageous commentary, because they love the subsequent outrage and attention it brings them," Ms Gorman said.
She said ignoring trolls didn't work and the best thing people could do to counter them was provide corrective information so lies don't get perpetuated.
A spokesperson for the Council of the Order of Australia said the council could recommend an award be cancelled, but would not comment on individual cases.
The regulations for the Order of Australia state the Governor General can rescind somebody's award for a variety of reasons including if it was deemed their actions bought disrepute to the Order.