Calls to revoke men's right advocate Bettina Arndt's Order of Australia honour are being weighed up by the body that co-ordinates the awards.
State and federal MPs are demanding Ms Arndt be stripped of the honour after she made controversial comments about the domestic violence murders of Hannah Clarke and her three children by her husband Rowan Baxter.
Governor-General David Hurley's office has referred their complaints to the Council for the Order of Australia.
Victorian Labor Attorney-General Jill Hennessy and Liberal Senator Sarah Henderson are among those who believe the honour should be revoked.
Ms Arndt drew scrutiny last week after tweeting "Congratulations to the Queensland police for keeping an open mind and awaiting proper evidence, including the possibility that Rowan Baxter might have been 'driven too far'."
Detective inspector Mark Thompson stood aside after also being criticised for saying the day after Wednesday's killing that officers were keeping an open mind as they piece together exactly what happened in the lead-up to the murders.
Det Insp Thompson said there were "probably" people in the community deciding "is this an issue of a woman suffering significant domestic violence and her and her children perishing at the hands of her husband? Or is this an instance of a husband being driven too far by issues that he's suffered by certain circumstances into committing acts of this form."
In a letter to Council for the Order of Australia chairman Shane Stone on Monday, Senator Henderson said Ms Arndt's comments have "brought disrepute on the order".
"These comments which concern a man who doused his wife and children in petrol and burnt them to death are abhorrent," she wrote.
The senator noted she has previously supported Ms Arndt for her "important contribution to the debate on family violence and gender equity".
"I believe that Ms Arndt has so seriously crossed the line in her commentary concerning this horrific act of family violence that it is no longer appropriate that she be awarded this honour," she said.
One Nation leader Pauline Hanson described the murders as a '"horrendous act" but said Ms Arndt should keep her award.
"She is clearly stating what she thinks and what a police officer said," she told Nine's Today Show.
Senator Hanson said she hoped an ongoing Senate inquiry into family law would help determine why people like Baxter committed such heinous crimes.
"A lot of people are driven to this, to do these acts, for one reason or another," she said.
"Hopefully the family law inquiry will get to the bottom of it, but don't bastardise all men out there, or women for that matter, because these things happen."
Ms Arndt was appointed a Member of the Order of Australia for "significant service to the community as a social commentator, and to gender equity through advocacy for men".
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