Australia's Prime Minister Julia Gillard has accused Opposition Leader Tony Abbott of being sexist and a misogynist, in a blistering counter-attack after he called for Speaker Peter Slipper to be sacked "immediately".

Mr Abbott wanted the Speaker removed, saying he was "no longer a fit and proper person to uphold the dignity of the federal parliament".

He told Australia's parliament yesterday that Mr Slipper was disqualified from the role "by the undenied, uncontradicted facts" that had emerged during a sexual harassment claim brought by the Speaker's ex-staffer James Ashby.

They included "truly gross references to female genitalia" and one showed a "clear bias" because it abused Liberal frontbencher Sophie Mirabella, Mr Abbott told parliament.


Peter Slipper resigned as Speaker late last night, leaving Labor's Anna Burke to become the country's third Speaker in three years and only the second woman to hold the position.

But Ms Gillard said the opposition leader had just discovered sexism because he wanted to use it as a battering ram against Mr Slipper.

She said his hypocrisy and double-standards should not be tolerated.

"I will not be lectured about sexism and misogyny by this man, I will not," Ms Gillard said, pointing at Mr Abbott.

"Not now, not ever."

She slammed Mr Abbott for his previous statements about abortion and women doing the ironing.

She also accused him of cat-calling her in parliament and stating she should, politically speaking, "make an honest woman of herself".

Ms Gillard also attacked Mr Abbott for standing next to a sign at an anti-carbon tax rally that read "Ditch the witch" and another which accused her of being former Australian Greens leader Bob Brown's "bitch".

"I was offended by those things - misogyny, sexism, every day from this leader of the opposition."

She said she was offended by the content of Mr Slipper's texts because she was always offended by sexism.

But parliament should wait for the Federal Court to deliver its judgement before MPs made up their minds about the Speaker, she said.

"People will then have an opportunity to make up their minds with the fullest information available to them."

"(So) this parliament today should reject this motion."

Earlier, Deputy Opposition Leader Julie Bishop said she would "personally struggle" to show appropriate respect for Mr Slipper if he again presided over question time.

"How the women in this house are expected to show respect to the Speaker when we are now aware of the views he holds of women is beyond comprehension," she said.

Mr Slipper left the Liberal party late in 2011 to take up the Speaker's chair, giving the minority Gillard government an extra buffer in the lower house.

He stood aside from the role in April pending an investigation into allegations he misused taxi vouchers.