Hours ahead of the potential censure for recent comments about there being no "good Muslims", the One Nation leader stormed out of the chamber after calling independent Lidia Thorpe a "bitch" on Monday.
The insult came amid a heated back-and-forth between the two during a debate on US-Israel strikes on Iran, during which Senator Thorpe continuously called Senator Hanson a liar.
She also castigated the One Nation leader for calling the US president "Senator Trump" during her speech.
The two then quietly traded barbs off-mic, with Senator Thorpe heard telling the firebrand, "if you want to talk to me, then make an appointment", before Senator Hanson used the derogatory term.
She walked out of the chamber as Senator Thorpe went to make a point of order over the comment, adding "I'll be glad to see the back of you in two years' time" in reference to the independent senator's plan not to contest the next election.
At least one coalition senator was seen trying to contain laughter.
Senator Hanson subsequently said she apologised "if the public heard me call Senator Thorpe a bitch", but added she didn't take back the comment.
"The Senate chamber is meant to be a place for debate, not constant screaming and yelling over the top of senators like we see from Senator Thorpe," she told AAP following the insult.
"I will not be repeatedly called a liar ... I've had a gutful of her and so too has the vast majority of Australians."
Senator Thorpe didn't wade in on the non-apology, saying Australians did not want more name-calling - they wanted action on rent, wages and the cost of living.
She accused the One Nation leader of focusing on culture wars to distract from her relationship with billionaires such as Gina Rinehart, including flying on the mining magnate's private jet.
"She's not standing up to the elites. She is part of them and then uses division and theatrics to distract from it," she said.
The heated exchange comes as the coalition faces pressure to reject a preference deal with the resurgent One Nation in an upcoming by-election for the NSW seat of Farrer.
The poll was triggered by the resignation of former Liberal leader Sussan Ley after she was knifed by Angus Taylor for the party's top job in February.
But Mr Taylor refused to say how the Liberals would direct preferences to One Nation, adding the party wasn't at that point yet.
"What I will say is we'll show respect to those who are thinking about voting One Nation," he told reporters.
The latest Newspoll, published on Monday, showed the coalition's primary vote rising slightly to 20 per cent, still well behind One Nation's 27 per cent and Labor's 32 per cent.
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