The Australian government has unveiled one of the world's most ambitious schemes to tackle climate change, a plan to tax carbon emissions from the country's worst polluters.

After a bruising political battle to win support for the measure, the prime minister, Julia Gillard, said on Sunday that from July next year, 500 companies would pay $23 (£15) a tonne for their carbon emissions in the largest emissions trading scheme outside Europe.

The government predicts that by 2029 the plan will lead to a reduction in emissions equivalent to taking 45m cars off the road. The government will fix the tax for three years, before moving to a market-set price in 2015.

"It's time to get on with this; we are going to get this done," said Gillard.

Australia generates more carbon pollution per head than any other developed country, thanks to its heavy reliance on coal-fired power stations. With a population of 22 million, Australia is responsible for 1.5% of global greenhouse gas emissions. By comparison, Britain, with nearly three times the population, produces just 1.7%.

The package is expected to pass votes in both houses of parliament before the end of the year, but Gillard faces a furious backlash over the scheme, which 60% of the population opposes. Her government is the most unpopular in 40 years, and analysts say her political future depends on her ability to sell the tax to voters.

"We've got to price carbon pollution to drive investment in innovation and to provide the incentive for energy efficiency," she said. "Failing to do so means that we would be passing on lower living standards to our children and grandchildren."

The scheme provides for a $10bn clean energy fund, money for a biodiversity fund, and – crucially for Gillard's political survival – compensation for voters.

The average Australian household will see its bills increase by around $10 a week, and critics of the plan say ordinary voters will be unfairly burdened by higher costs passed on to them by the big polluters.

But Gillard said 50% of the scheme's revenue would be returned to households in the form of tax cuts and compensation worth more than $15bn. Two-thirds of all households would receive enough assistance to cover the entire financial impact of the tax, Gillard said.

"This is pitched at low-income families because we know their budgets are tight," she said. "I want people to understand that we are seizing a clean energy future."

Before last year's election Gillard explicitly ruled out a carbon tax, in an attempt to distance herself from her predecessor, Kevin Rudd, who failed to get an emissions trading scheme through parliament. But she changed tack after the election returned a hung parliament and she had to build an alliance with the Green party.

The leader of the opposition, Tony Abbott, has denounced the tax as "socialism masquerading as environmentalism" and called for an election which he said would be a referendum on the scheme.

"It's a package which is all economic pain for no environmental gain," he said on Sunday.

Australia's parliament has twice rejected attempts to introduce a carbon emissions trading scheme. A high-profile campaign against the tax could further undermine the government, which faces elections in 2013.

"I think this package is going to compound the trust issue which has dogged the prime minster ever since she assassinated Kevin Rudd and has dogged her since she was deceptive about the carbon tax before the last election," said Abbott.

Australia is the world's biggest exporter of coal and iron ore, and its powerful resources sector is the bedrock of the buoyant economy.

The tax package includes compensation for many trade-exposed industries, including steel and aluminium, with up to 94.5% of their permits granted for free. Moderate emitting exporters will get 66% of permits for free.

But the Minerals Council of Australia says the resources sector will suffer a $25bn hit by 2020, with around 20,000 job losses.

"This is taking a baseball bat to the Australian economy to raise another tax which will be a dead loss to the economy without any benefit to the environment," said the council's chief executive, Mitch Hooke.

The Greens have been central in months of negotiations over the tax. Gillard relies on them to govern and, as of last week, they also control the balance of power in the upper house.

The Greens' deputy leader, Christine Milne, said: "This is the moment where Australia turns its back on the fossil fuel age, and turns its face towards the greatest challenge of the 21st century, and that is addressing global warming."