Liberal Senator Jonathon Duniam said there are never any excuses or justifications for family violence.
"We will support this motion (because) comments like those expressed by Ms Arndt are abhorrent and unacceptable," he told the Senate.
But he clarified the government does not make decisions to award or cancel the honours and respected the independence of the Council for the Order of Australia.
Labor frontbenchers Penny Wong and Kristina Keneally had moved the motion on Tuesday calling on senators to jointly condemn Ms Arndt's comments as "reckless and abhorrent" and strip her of the honour.
"The values that underpin Ms Arndt's views on this horrific family violence incident are not consistent with her retaining her Order of Australia," the senators said in their motion.
Hannah Clarke, 31, died at the Royal Brisbane and Women's Hospital after she and her children were doused in petrol by her estranged husband and the children's father, Rowan Baxter, 42.
One Nation senators were the only voices against the motion, with Senator Pauline Hanson defending Ms Arndt's support for Queensland detective inspector Mark Thompson.
Bettina Arndt had tweeted: "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'."
Senator Hanson said Detective Inspector Thompson's comments had been "unscripted" as he tried to address both the media and public disbelief over the murder-suicide of Ms Clarke and her young family.
"It is the role of the police to investigate this unconscionable incident and that may very well include triggers that led to the event – on the 19 of February," she said.
"No right-thinking person condones the actions of domestic violence and this was one of the country’s worst.
"Bettina Arndt has the right to support the role of police and in particular Detective Inspector Mark Thompson."
Senator Kristina Keneally made clear the motion was against Ms Arndt's comments and "in no way" made comment or condemnation against the Queensland police.
"This motion has been carefully crafted to make clear the concern expressed and I hope expressed by this chamber is with the comments of Ms Bettina Arndt only," she said.
Earlier, she had urged her upper house colleagues to "stand firm" and make it clear there was no excuse for family violence.
"There is no excuse for what happened to Hannah Clarke and her three children, it was a murder plain and simple, but there is nothing plain and simple about the tragedy that is domestic violence," she told reporters.
"And there is nothing plain and simple about using your position with an Order of Australia to spread comments that could be seen to be inciting violence, that seem to be condoning violence."
Senior government minister Peter Dutton also called out Ms Arndt's remarks but would not say whether her award should be revoked.
"I don't agree with the comments," he told reporters.
Liberal senators Sarah Henderson and Hollie Hughes have also spoken out against Ms Arndt.
Governor-General David Hurley has forwarded complaints about her Order of Australia to the body that manages the awards.
Queensland's Police Commissioner has since asked detective inspector Mark Thompson, who was leading the investigation into the murder-suicide in Brisbane to step aside from the investigation.