The opposition is pushing to ram through a ban on Nazi symbols after a protest in Melbourne drew neo-Nazis, who used the Sieg Heil salute.
Liberal frontbencher Michaelia Cash said the push to ban the symbol needed to take precedence.
"Every Australian should find the actions of that small group of protesters who dared to use the Nazi salute offensive," she said.
"Those who display Nazi symbols or use the Nazi salute are either ignorant of the past or are deliberately promoting evil."
Finance Minister Katy Gallager said there is no place in Australia for Nazi ideology.
"But I think we should also acknowledge this is a complex area of law and any move to ban Nazi symbols deserves serious consideration," she said.
"The Australian people deserve better. We should stand together, we should send a strong voice about the events we saw in Victoria.
"This bill needs serious consideration, not a stunt."
But Greens senator Sarah Hanson-Young shot back, saying politicising the issue would drag the debate into the gutter.
"I don't think anything we've displayed to the Australian people ... is anything to be proud of," she said during the debate.
"The politicking over this issue - which is serious, which is sensitive, which is fundamentally about the values of a respectful, democratic nation - should not be drawn into the gutter."
Liberal senator Sarah Henderson cried in the chamber after an interjection from Labor minister Murray Watt.
Senators in the chamber said the interjection related to text messages she sent the Victorian Liberal leader, who is trying to expel a state MP for attending the Melbourne anti-transgender rights rally where Nazis showed up.
"I am disgusted in you," a crying senator Henderson yelled across the chamber.
The push to have the bill debated ultimately failed, with all sides agreeing it was an important issue to discuss, but Labor, the Greens and One Nation accusing the opposition of bringing it on as a last minute stunt.
"There should be time to debate this, not cut off. I believe every member in the house will vote to get rid of Nazi symbols," One Nation leader Pauline Hanson said.
"Just stop your politicking in this place ... and throwing mud at each other."
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