Abbott, whose Liberal-National coalition is leading in polls before elections due next year, has faced claims from Labor ministers that he has a problem dealing with powerful women. He began a media blitz defending his credibility last week with the help of his wife Margie.
Gillard has been confronted by protesters bearing placards reading "Ditch the Witch" since becoming prime minister in June 2010, and has previously attacked sexism in Australian politics. Tuesday, she accused Abbott of "repulsive double standards when it comes to misogyny" and said she'd been offended by "cat-calling" to her in the House of Representatives.
Opposition lawmakers including Nationals leader Warren Truss said the government is trying to undermine Abbott to deflect attention from a slowing economy and the introduction of new taxes.
Gillard is the first Australian prime minister who isn't married. She has no children and lives in the capital Canberra with her partner, hairdresser Tim Mathieson. In August, she said there were sexist overtones to allegations she was guilty of misconduct at a law firm she worked at in the 1990s.
Australia has a "blokey" culture, and Gillard plans to boost female representation across government boards, she said in an interview in September 2011.
While retaining the title of speaker, Slipper hadn't served in the role since April, when he stepped aside after a former employee issued a civil claim accusing him of making unwanted sexual advances. He is fighting the civil action.
Slipper, 62, held the seat of Fisher in Queensland, which he won in 1993, for the Liberal Party until November, when he resigned from the party to become an independent and was named Speaker.
"The importance and the role of the House of Representatives in Australia is far more important than my own future or my own continuation as speaker," Slipper said in an address to parliament Tuesday. He said he will remain an independent lawmaker and was confident he would be vindicated.
Anna Burke, a Labor lawmaker, was elected by the House to replace Slipper as speaker. The resignation isn't expected to negate the minority government's ability to push legislation through parliament, Leader of the House Anthony Albanese, told Australian Broadcasting Corp. in an interview.
Abbott Tuesday claimed Labor should have "died of shame" for its performance in governing. His words echoed those of Alan Jones, a critic of Gillard, after the Sydney-based disc jockey claimed at a Liberal Party fundraiser that the prime minister's father, who passed away last month, had "died of shame."
Abbott has declined to rule out appearing on Jones' radio show, which has suspended all advertising after companies withdrew their support.
"The government is not dying of shame," Gillard said Tuesday. "My father did not die of shame. What the leader of the opposition should be ashamed of is his performance in this parliament and the sexism he brings with it."
Gillard joined senior Labor lawmakers including Attorney-General Nicola Roxon and Health Minister Tanya Plibersek in claiming Abbott has a problem dealing with powerful women. The opposition leader last month denied allegations that he physically intimidated a female political opponent during Sydney University elections in 1977.
The latest analysis of Newspoll surveys, published in The Australian on Oct. 5, showed 29 percent of female voters are satisfied with Abbott, compared with 34 percent of men.
"I won't stand by and let others claim that the man I love, and the father my children adore, has some agenda against women," Margie Abbott said in a News Ltd. interview published Oct. 5.
Support for Gillard's governing Labor Party has fallen from an 18-month high, as the prime minister struggles to gain traction with voters before elections due next year.
Labor's primary vote dropped 3 percentage points to 33 percent, while Tony Abbott's Liberal-National coalition climbed 4 points to 45 percent, according to a Newspoll survey published in the Australian newspaper Tuesday. Taking preference votes into account, Labor trailed the coalition by 8 points after pulling level in the previous survey.