Independent senator David Leyonhjelm wants Prime Minister Malcolm Turnbull to call out hatred of men as he continues to defend his heated remarks about Sarah Hanson-Young’s personal life.

The NSW senator has also accused his female Greens counterpart of being the worst offender of using unparliamentary language, saying she is regularly forced to withdraw statements while he is not.

Senator Leyonhjelm also stood by his previous description of the Prime Minister as a “pussy”, branding Mr Turnbull a doormat for rolling over on misandry.

“Misandry is equally as bad as misogyny. He should also call out misandry. It’s equally as bad, it’s also sexism,” he told ABC radio on Wednesday.

The Liberal-Democrat senator’s challenge comes after Mr Turnbull called on him to apologise for telling Senator Hanson-Young in parliament to “stop shagging men” and alluding to her private life in subsequent media interviews.

Senator Leyonhjelm defended himself again on Wednesday, saying it was silly to suggest he had a problem with powerful women.

“I will tell people they’re bastards or bitches or to f-off regardless of their gender. It is normal Australian behaviour,” he said.

“I don’t discriminate between men or women.”

Senator Hanson-Young this week said she had put up with sexist comments in parliament for years. But the “slut-shaming” from Senator Leyonhjelm went too far.

She wants to stamp out sexism in the workplace, and has asked men around Australia to realise what women go through.

“If you see it happening to a woman, if you hear it happening to your sister, to your mother, to your work colleague, say something,” an emotional Senator Hanson-Young said on Tuesday.

“Stand up and say something, because I can guarantee you she’s not having fun.”

But Senator Leyonhjelm believes Senator Hanson-Young is herself a sexist who thinks all men are responsible for violent crimes against women.

“Every week, pretty much without exception, she uses unparliamentary language – she abuses people,” he said.

He denied “slut-shaming” the South Australian senator.

Senator Hanson-Young has fired off legal letters to Senator Leyonhjelm, and Sky News and Melbourne radio station 3AW for their subsequent interviews with him about the verbal stoush. She has not yet said if she will sue for defamation.

Labor leader Bill Shorten has also called on Senator Leyonhjelm, who is continuing to stand firm, to apologise.

The blue began during a Senate debate last week on a motion calling on the government to allow women to carry tasers, pepper spray and mace to defend themselves from murderers and rapists.

Senator Leyonhjelm said he thought he heard Senator Hanson-Young say words to the effect of “all men are rapists” and he responded with “stop shagging men”. She denies making the statement.

When Senator Hanson-Young approached him afterwards, he confirmed his comment, she called him a creep and he told her to “f— off”.