Attorney General George Brandis insists no one in the government will break ranks over changes to race-hate speech laws.
Aged Care Minister Ken Wyatt in the past has vowed to cross the floor of parliament and vote against the government over the issue.
"I am absolutely certain that every member of the coalition will be voting for these changes ... every last one of them," Senator Brandis told the the Senate on Tuesday.
Greens leader Richard Di Natale seized on the timing of the government's announcement on Harmony Day.
"What's next? Are you going to use White Ribbon Day to cut funding for domestic violence services, again?" he asked Senator Brandis.
Senator Di Natale queried whether International Children's Day was an opportunity to scrap child labour laws?
The attorney-general responded by saying he was disappointed by such a "cheap political point" about violence against women.
Labor senators heckled Senator Brandis for wearing an orange Harmony Day ribbon, calling on him to remove it as he defended the changes to race-hate laws.
Indigenous Labor senator Malarndirri McCarthy asked the attorney-general what it was he wanted to be able to say to people like her or others from different races.
"As a white man growing up in Petersham and attending private schools I'm sure you've never been denied access or service to a shop," she said.
"You've never had taxis drive past pretending not to see you, you've never received hateful letters or emails because of your race or the colour of your skin.
"I really wish I could believe there aren't any racists in Australia but certainly my personal experience, my family's experience, informs me of the reality that I live in this country."
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