Health Minister Greg Hunt, who has been spoken of as a possible future prime minister, let rip at Fay Miller, the mayor of the northern town of Katherine, during a meeting in December.
As well as swearing, he was accused of intimidating her by wagging his finger in her face.
Hunt only apologised after Miller wrote a letter to Prime Minister Malcolm Turnbull highlighting his "unwarranted, disrespectful and unacceptable behaviour".
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"During the course of the conversation, I used strong language," Hunt admitted.
"I have apologised to the mayor of Katherine and today I want to repeat that apology publicly and sincerely, and absolutely."
Asked in parliament if he had been involved in any other similar incidents, Hunt said one other case had been raised with him regarding a "strong discussion" he had with a former health department secretary.
Hunt's outburst against Miller came when she suggested more funding to deal with contamination arising from the use of fire-fighting foam in her region.
He replied that she would need to take it up with Northern Territory senator Nigel Scullion.
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Miller said in her letter to Turnbull that at that point, she told Hunt "Senator Scullion comes to Katherine but I don't see him".
"He (Hunt) relocated his chair, pointing towards me and said 'you need to fucking get over it, you need to fucking make Senator Scullion your best friend'," Miller wrote.
"I didn't move. I was absolutely totally gobsmacked," she added.
Miller told ABC radio Hunt's next two sentences also contained the F-word.
"And then he sat back a little in his chair and said, 'I've heard you're feisty'," she said.
"And I thought, 'Really?' I hadn't said a word, not a word at this stage, because I was in such a state of shock at what he was saying."
Asked by the ABC how she found Hunt's attitude, Miller replied: "That was misogynist."
Former prime minister Julia Gillard famously accused her opposition counterpart Tony Abbott of misogyny in a fiery parliamentary speech in 2012 that went viral.
She later spoke of her "murderous rage" at her sexist treatment while in politics.
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