Opposition leader Tony Abbott challenged on Thursday Australian Prime Minister Julia Gillard to resign because of her inability to protect the country's borders.

"A prime minister who is incapable of protecting the borders of our country is a prime minister who has manifestly failed in the highest task she has," News.com.au quoted Mr Abbott.

"Frankly, it is a government and a prime minister who should resign - not engage in the kind of vituperation that I am sure we are going to get again and again in this parliament on this matter," Mr Abbott said.

He made the challenge amid the quashing by Australia's High Court of the government's ability to enter into an asylum seeker agreement with Malaysia or any other country. Mr Abbott also pointed to the prime minister's contrary stands for offshore processing and temporary protection visas.

He cited statements from Ms Gillard dating back to 2002 when she expressed both opposition and support for offshore processing. Mr Abbott accused the prime minister of showing support for every policy because "she believes in nothing."

Mr Abbott criticized the government-proposed Malaysia deal for lack of human rights protection for asylum-seekers. He pointed out the coalition's counterproposal to bring back processing in Nauru would protect the human rights of foreigners seeking asylum while strengthening Australia's boundaries.

Debate is ongoing at the House of Representatives over the government-sponsored legislation which aims to go around the High Court ruling that declared the Malaysia refugee swap unlawful. Instead of waiting until October to debate on the amendments, Labor moved the debate earlier to Thursday.

Labor Parliamentary Secretary Richard Marles accused Mr Abbott of peddling rank politics. He said the coalition stand is "a total abandonment of any desire to pursue public policy."

"They desperately hope that in the pursuit of solving a very complex problem, that this country fails. They are precisely voting for failure," The Australian quoted Mr Marles.

Labor frontbencher Bill Shorten said that talks of pressuring to oust Ms Gillard as Labor Party leader is "a Liberal beat-up." Mr Shorten, one of the political leaders behind the ouster of former Prime Minister Kevin Rudd from his post in June 2010, said he is unaware of any move to boot out Ms Gillard from the top party leadership post.

Greens leader Bob Brown said the party is against offshore processing, but would neither support the Labor legislation nor the opposition amendments.