Australian Prime Minister Julia Gillard has dared her political rival, former foreign minister Kevin Rudd, to challenge her in a leadership vote next week, hoping to end infighting that threatens to sink the minority government and its reform agenda.

Gillard called on Thursday for the vote to be held by ruling-party lawmakers next Monday, gambling that a victory for her would silence Rudd whom she accused of trying to destabilise her unpopular government and regain the top job.

The Gillard-Rudd rivalry has been brewing since she replaced him as prime minister in a late-night coup in 2010. It burst into the open on Wednesday when Rudd quit as foreign minister while on a trip to Washington, saying he could no longer work with Gillard and that she could not win the next election, due next year.

Following Kevin Rudd's resignation yesterday, I have formed this view that we need a leadership ballot in order to settle this question once and for all, Gillard told reporters, keeping composed and trying to contrast Rudd as a chaotic leader.

For far too long, we have seen squabbling within the Labour Party. Australians are rightly sick of this, and they want it brought to an end, she said.

Gillard said she expected Rudd to stand for the leadership, though he had yet to declare whether he would contest.

Most analysts believe, however, that any changes would not save the party from defeat at the polls.

Labour is going to lose the next election. The current government can't get itself out of the doldrums and this is likely to drag on for the rest of the year, Sydney University political analyst Peter Chen said.

If Labour changes to Kevin Rudd, they will find his support is much softer than people think, he said, adding that if Rudd lost the vote, he would remain a divisive and destabilising figure within the government.

ODDS AGAINST RUDD

A Monday vote limits Rudd's ability to build sufficient support to replace Gillard. Rudd is travelling back to Australia from Washington, where he was on an official visit when he suddenly quit as foreign minister.

I'm very pleased and encouraged by the amount of positive support and encouragement of me to contest the leadership of the Labour Party, he said in a televised news conference from Washington before boarding a flight home.

Opinion polls show Rudd remains more popular with voters but is not well liked by party MPs, who select their leader.

Gillard is backed by most of them, including most senior cabinet members, making it unlikely Rudd can mount a successful challenge.

If, however, he did win, Rudd would have to renegotiate deals with the Greens and at least two independents to keep the government's one-seat majority in the hung parliament.

If he couldn't, he would have to call an early election which Labour would probably lose, putting at risk the future of key reforms such as a carbon tax and 30 percent tax on coal and iron ore mine profits, both due to start on July 1.

Opposition Leader Tony Abbott has vowed to scrap the mining tax and carbon tax if he wins power.

TRUST, POLICY, VISION

Senior government ministers rallied behind Gillard on Thursday, led by Deputy Prime Minister and Treasurer Wayne Swan, who cancelled a planned trip to Mexico for a G20 finance ministers' meeting.

I believe there is very strong support for the prime minister, he told Australian radio, saying Rudd was running a stealth campaign to undermine Gillard's leadership.

Other senior ministers also expressed support for Gillard.

We need to get out of this idea that Kevin is a Messiah who will deliver an election back to us. That is just, I think, fanciful, Attorney-General Nicola Roxon said.

But Immigration Minister Chris Bowen and Resources Minister Martin Ferguson, both senior cabinet ministers, publicly supported Rudd.

In my opinion, Kevin Rudd is best placed to take on Tony Abbott and potentially in the best position to win the next election, Ferguson told reporters.

(Additional reporting by Paul Eckert in Washington, and Maggie Luyueyang in Canberra; Editing by Lincoln Feast and Jonathan Thatcher)