Kevin Rudd, who stepped down as Australia's foreign minister this week, said on Friday he would contest a leadership vote against Prime Minister Julia Gillard, bringing to a head a bitter leadership fight engulfing the minority government.

Rudd, who was ousted as prime minister by Gillard in June 2010, said Australians had lost trust in Gillard and the party was headed to an electoral wipeout at the next elections, due in late 2013, under her leadership.

I want to finish the job the Australian people elected me to do when I was elected by them to become prime minister, Rudd told reporters.

Gillard called a leadership vote for Monday after Rudd quit as foreign minister on Wednesday, hoping the early vote would enable her to stamp her authority over the Labor Party and head off Rudd's hopes of building support.

But the vote has opened deep divisions within the government, split the cabinet over which leader to support, and unleashed a wave of criticism against both Rudd and Gillard from the warring factions.

The leadership crisis was sparked by poor opinion polls which show the government would be decimated at the next election, losing up to 15 seats. Labor's popularity has plunged under Gillard because of the introduction of contentious legislation and concessions to independent lawmakers and the Greens.

Gillard's supporters say she has clear majority support within the Labor Party and bookmakers believe she would easily win a leadership showdown against Rudd. She has called on Rudd to abandon any leadership ambitions if he loses.

Polls show Rudd remains more popular with voters, and he has called for Australians to lobby their members of parliament to support his campaign to return as prime minister.

Rudd said he would remain in parliament and would not mount a second challenge if he loses on Monday.

A surprise Rudd victory could spark an early election, as there is no guarantee he will win the backing of independents needed to control a majority in parliament. That, in turn, would risk major reforms, including a carbon tax and a 30 percent tax on coal and iron ore mines.

Opinion polls show the conservative opposition would easily win an election, and opposition leader Tony Abbott has promised to scrap the carbon tax and mining tax if he wins.

Markets, which rarely react to political developments in Australia, have largely ignored the dispute, seeing little difference in policies and expecting the uncertainty over the leadership to be resolved.

The bottom line is it's still a Labor government and the Labor government policies are still in place, said Annette Beacher, head of Asia Pacific research at TD Securities in Singapore.

Gillard told reporters that she had the strength, temperament, courage and character to lead Australia, and that she had pushed through major reforms where Rudd failed.

This is not an episode of Celebrity Big Brother, this is about who should be prime minister, Gillard said, adding she was confident she could lead the party to victory at the next election.

Gillard replaced Rudd in an internal coup in June 2010 and then went on to win dead heat elections, forming a minority government with support of the Greens and independent lawmakers.

Rudd said Gillard had betrayed him in 2010, backing down on an agreement to give him more time to restore Labor's poll standing while secretly plotting with faction leaders to replace him.

If he wins the leadership vote, Rudd would need to renegotiate agreements with the Greens and at least two independents to ensure he could control a majority in parliament.

There are few major policy differences between Rudd and Gillard, although Rudd has said he would do more to build business confidence in Australia, help manufacturers, and focus on health and education.

He also said he would review the transition from a fixed carbon tax, due to start at A$23 ($24.60) a tonne, to a full emissions trading scheme, possibly bringing forward carbon trading from its planned starting date in 2015.

The carbon tax applies to Australia's 500 top polluting companies, but industry has complained that the price is too high compared with the price of carbon permits in Europe.

I think it is important to look carefully at how the implementation of the current tax goes in its first six months, Rudd told reporters, without giving details.

The powerful Minerals Council of Australia, representing the country's biggest mining companies, called on Rudd to quickly rethink the carbon tax if he regains his old job.

He should not wait to review it in six months if he becomes prime minister on Monday, he should do it immediately, Mitch Hooke, the council's chief executive said.

(Editing by Lincoln Feast and Robert Birsel)