The Labor-led government wants to push ahead with the Malaysian people-swap deal while the Coalition insists on its proposal to establish offshore processing in Nauru, conflicting ideas that independent MP Rob Oakeshott says can be fused by his bill.

And by ensuring the addition of human rights protection guaranteed by federal authorities, Mr Oakeshott told the Parliament on Tuesday that it should approve his bill, which he stressed was not a copycat of any previous legislation on the controversial matter but rather a compromise that would save lives and allow the government to perform its normal job.

"This is as much as anything (about) trying to stop the loss of life at sea of people trying to get to Australia ... and this is attempting to try and break criminal syndicates ... involved in the insidious trade of people smuggling," Mr Oakeshott told his colleagues.

In her response, Prime Minister Julia Gillard conceded that the private bill could serve as a 'circuit breaker' in the political deadlock that has been characterising the Parliamentary debate on how to tackle the asylum-seeker problem that confronts Australia.

Last week, up to 100 people were feared dead by authorities as a crowded boat of refugees that was trying to reach Christmas Island capsized.

Another boat, according to The Daily Telegraph, met tragedy on Wednesday almost in the same area of the disaster last week though most of the passengers, mostly women and children, have been rescued by the Australian Navy.

Citing reports from the Australian Maritime Safety Authority, Ms Gillard reported to the Parliament that 123 out of the alleged boat people have been rescued so far.

She could not confirm if lives were again lost or people remain missing, stating "here in the parliament now, I simply don't know."

Hopefully, Ms Gillard added, such tragic incidents will never happen again as she stressed "I have reason to believe that the bill moved by Mr Oakeshott may be in a position to command majority support in this House of Representatives."

She called on all MPs to look beyond their respective party stands and take a second look on the Mr Oakeshott's bill as and by doing so they can claim that they contributed in ending once and for all the unnecessary loss of lives.

"As a Labor leader, I would want to walk from this place saying 'no one won, no one lost - we just got something done," the Prime Minister was reported by the Australian Associated Press (AAP) as saying.

Opposition Leader Tony Abbott agreed that the present situation call for the brushing aside of partisan politics but insisted it is next to impossible for "anyone on either side of this parliament would expect people to put aside their strongly held beliefs ... on the question on border protection."

Mr Abbott asked for more time for the Coalition to rethink is stance on the matter but Ms Gillard rebuffed him by saying, "the eyes of the nation are upon us, given this second incident with an asylum seeker vessel, and nothing is to be gained by delay."

The Liberal leader conceded that "the Australian parliament do what it can to deliver a stronger policy response," in light of the second boat disaster in as many weeks but insisted that the House should also consider his private bill that would allow only offshore processing on territories of countries that were signatory to the UN refugee convention.

His bill automatically writes off the Malaysian solution being advocated by the government since Kuala Lumpur was not a party to the UN-sponsored principle.

On his part, Liberal frontbencher Malcolm Turnbull called on Ms Gillard to make some concessions for the Parliament to finally resolve the sticky issue this week, the prospect of which could save lives, he added.

She can do so, Mr Turnbull added, by testing the Nauru processing and if it flopped then she'll have a stronger case for the Malaysian solution in the immediate aftermath.

Besides, the former opposition leader said, the Oakeshott bill "can never be law," because the Coalition and the Australian Green will surely kill the proposal in the Senate.

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