TONY Abbott has accused the government of double standards on the women's issue as the Coalition increases pressure on Julia Gillard to declare a stand on Speaker Peter Slipper's offensive sexist text messages.

Mr Abbott said it was very reasonable to ask how Ms Gillard could on one hand have her ministers claim he was ''somehow anti-woman'' when she had made Speaker someone who had been disrespectful towards women.

In messages to his then-staffer James Ashby that have come out in the current court action, Mr Slipper referred to female genitalia as ''shell-less mussels''.

Mr Abbott told 3AW he would not go into all the text messages that were now sweeping into the public arena.

''But plainly, I think there are legitimate questions. How can Nicola Roxon and how can Julia Gillard continue to support a Speaker who has that kind of attitude towards women?'' he said. ''It's pretty obvious that this bloke has shown considerable disrespect towards women.''

Deputy Opposition Leader Julie Bishop said the issue was ''a real leadership test for Julia Gillard''. ''If she is so concerned with what she terms 'sexist' and 'misogynist' behaviour, then she cannot possibly maintain her support for Peter Slipper as the Speaker.''

Ms Gillard has not yet been questioned on the text messages; Attorney-General Roxon has indicated her distaste but declined to comment because the Ashby sexual harassment case against Mr Slipper is still going.

Ms Bishop said the text messages made Mr Slipper's position untenable. ''There are numerous of them about women'' indicating ''a very obscene, extreme, degrading view of women. I would find it difficult to appear in the House of Representatives and show respect for a Speaker who holds those views and expresses those views about women,'' Ms Bishop said.

The government has supported Mr Slipper's return to the chair in the House of Representatives if he is cleared in the Ashby case and also of allegations of misusing Cabcharges.

Ms Bishop said the government's line - that it would not comment because the case was still on - was a ''fig leaf''.

She said Ms Roxon had made comments about the case and called Mr Ashby a vexatious litigant. ''It was all very well for them to comment on the Slipper/Ashby case when they thought they had a political point to make. They are now stuck with the fact that Peter Slipper was their choice of Speaker.''

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