A fiery speech in which Australia's Prime Minister Julia Gillard accused the opposition leader of being sexist and misogynistic has gone viral.

Gillard launched a blistering attack on Tony Abbott, saying: "I will not be lectured about sexism and misogyny by this man, I will not. And the Government will not be lectured about sexism and misogyny by this man."

She added: "If he wants to know what misogyny looks like in modern Australia, he doesn't need a motion in the House of Representatives. He needs a mirror."

Her tirade came after Mr Abbott called for the dismissal of the speaker, Peter Slipper, over lurid text messages he sent to a former member of staff.

Gillard then accused Abbott of possessing double standards when it came to sexism, saying: "I was offended when the leader of the opposition went outside in the front of Parliament and stood in front of a sign that said 'ditch the witch'. Misogyny, sexism, every day from this leader of the opposition."

Abbott told local media on Wednesday that it was time to move on from the outburst: "I think it's time that everyone in the parliament moved on from this gender card which so many members of the Government have been playing."