Canberra - Australian Labour Prime Minister Julia Gillard will know on Tuesday if she can form a new minority government with the support of three independents, ending more than two weeks of uncertainty after the August 21 elections.

Independent Tony Windsor said the impasse should end on Tuesday morning, but there was a risk the three independent MPs could still split, delivering a deadlock of 75 votes apiece in the 150-seat lower house and the prospect of another election.

But in a further setback for conservative opposition leader Tony Abbott, the independents said they will not make a final choice until he confirms support from a rebel National Party MP who wants to sit on the cross benches in the new parliament.

Gillard and Abbott have been desperately wooing the independents for their support for a minority government since August 21 elections delivered the country's first hung parliament since World War Two.