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CANBERRA—Australian Prime Minister Kevin Rudd stepped down on Thursday, amid a mutiny in the once-popular leader’s governing party, clearing the way for the country’s first female prime minister.

Getty Images , European Pressphoto Agency Julia Gillard stood unopposed for the party leadership after Mr. Rudd resigned.

Mr. Rudd resigned before a leadership ballot could be held, after Deputy Prime Minister Julia Gillard, a Welsh-born 48-year-old former trial lawyer, challenged him for the top spot in the governing center-left Labor Party—a post that carries with it the premiership. Ms. Gillard stood unopposed at Thursday’s vote of Labor’s 112 lawmakers.

Ms. Gillard’s candidacy was backed by the Labor Party’s right wing, but also by key unions on the left.

Her challenge marks an unprecedented fall for the man who ended nearly 12 years of conservative government in Australia. Mr. Rudd swept to power in November 2007, ousting the long-ruling Liberal-National coalition of center-right parties. His popularity slid in recent months after a series of policy missteps.

The party feared that Mr. Rudd, a 52-year-old Chinese-speaking former diplomat, would lead them to defeat in national elections that could come as soon as August.

“In Australian politics, it is almost unprecedented that a first-term prime minister is dumped by his own party,” said Roland Randall, a strategist at TD Securities in Singapore.

But Mr. Randall said in a note to investors that “for markets, this should not be a destabilizing event,” because Mr. Rudd and Ms. Gillard aren’t far apart on policy.

Driving Mr. Rudd’s reversal have been a decision to shelve a proposed carbon cap-and-trade system meant to fight climate change and a planned tax on “super profits” by Australia’s mining companies—a critical industry for the resource-rich country.

The tax, which the government thought would win popular support by spreading the wealth from the booming mining sector, has instead backfired as the public worries it will damage Australia’s credibility as an investment destination. Mining giants BHP Billiton Ltd. and Rio Tinto Ltd. warned that billions of dollars of investment are at risk, and they have led a fight against the 40% levy, saying it would make Australia one of the highest-taxed jurisdictions in the world.

This criticism has resonated with many Australians who own shares in mining companies, often through pension funds.

Mining, a top export sector, helped Australia sidestep the global recession, thanks to demand from developing countries like China and India for the country’s vast stores of iron ore and coal.

Unlike Mr. Rudd, said Mr. Randall, the strategist, Ms. “Gillard has not been steadfastly inflexible in her position and would not look weak if she chooses to compromise on the tax.”

The Australian dollar rose on the news against the U.S. currency, and Australian stocks gained, led by mining companies, on hopes that Ms. Gillard would soften the tax. The S&P/ASX 200 was up 0.6% in Thursday morning trading.

“As you would expect after Rudd’s departure, resources stocks are outperforming…Obviously it’s giving people some hope that the resources super profits tax will be altered,” said Chris Blair, a senior private client adviser at brokerage Patersons.

BHP Billiton was up 2% and Rio Tinto gained 2.4% in morning trading. T

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Still, Wednesday’s political uprising came as a shock. As recently as Monday, Finance Minister Lindsay Tanner said talk of Ms. Gillard taking on Mr. Rudd was “complete nonsense.” Just hours before Mr. Rudd’s news conference on Wednesday night, key Labor figures were denying that any challenge was afoot.

On Wednesday, Mr. Rudd sought to portray himself as above party squabbles. “I was not elected by the factional leaders of the Australian Labor Party to do a job—though they may be seeking to do a job on me,” he said. He emphasized his stewardship through the global financial crisis, which Australia shrugged off with only a brief slowdown in economic growth.

The prime minister said he was “fundamentally proud” of “navigating this economy through the worst crisis the world has seen” and of “keeping hundreds of thousands of Australians in jobs that would otherwise have been on the unemployment queue.”

Mr. Rudd’s plight would have been unthinkable a year ago, when his approval rating was well above 60%.

A poll earlier this week found Labor eking out a 52% to 48% edge against the Liberal-National bloc, calculated on the basis of Australia’s preferential voting system. On a straight matchup, Mr. Rudd’s party was trailing 40% to 35%.

Critics said Mr. Rudd has squandered the political goodwill awarded to him for bringing Labor in from the political wilderness with a landslide victory. The career bureaucrat’s aloof demeanor and tendency to immerse himself in policy has drawn parallels with President Barack Obama, with whom he struck up an early friendship.

Mr. Rudd’s tendency to announce rather than consult with the party on policy also irked some. It may have made it easier for his detractors to level blame and ultimately undermine him once his authority was called into question.

Ms. Gillard, elected to Parliament in 1998, has risen swiftly through the Labor ranks and held the key portfolios of education, employment and workplace relations.

She has shown sharp political elbows in the past. When a political opponent said in 2007 that the unmarried lawmaker wasn’t qualified to lead the country because she had chosen not to have children, Ms. Gillard shot back that her accuser was “a man of the past, with very old-fashioned views.”