By Jane Wardell

SYDNEY (Reuters) - Australian Prime Minister Tony Abbott's chief business adviser has accused the United Nations of using debunked climate change science to lead a new world order, provocative claims made to coincide with a visit from the top UN climate negotiator.

Christiana Figueres, who heads the UN Framework Convention on Climate Change, toured Australia this week, urging the country to move away from heavily polluting coal production.

Under Abbott's leadership, Australia has been reluctant to engage in global climate change politics, unsuccessfully attempting to keep the issue off the agenda of the Group of 20 Leaders' Summit in Brisbane last year.

Maurice Newman, the chairman of Abbott's business advisory council and a climate change skeptic, said the UN was using false models showing sustained temperature increases to end democracy and impose authoritarian rule.

"The real agenda is concentrated political authority," Newman wrote in an opinion piece published in The Australian newspaper on Friday. "Global warming is the hook.

"It's about a new world order under the control of the UN," he added. "It is opposed to capitalism and freedom and has made environmental catastrophism a household topic to achieve its objective."

Figueres used an address in Melbourne to urge Australia to move away from coal, the country's second-largest export, as the world grapples with global warming.

"Economic diversification will be a challenge that Australia faces," she said.

Abbott has described coal as "good for humanity" and the "foundation of prosperity" for the foreseeable future.

Figueres also urged Australia to play a leading role at the climate summit in Paris in December, a call unlikely to be heeded given Abbott's track record.

At the Brisbane G20 meeting, Abbott warned that the Paris summit would fail if world leaders decided to put cutting carbon emissions ahead of economic growth.

At home, Abbott, who in 2009 said the science behind climate change was "crap", repealed a tax on carbon pricing and abolished the independent Climate Commission advisory body.

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Asked on the Canberra leg of her trip if the politics around renewable energy was as toxic elsewhere in the world, Figueres said: "No. At the global level what we see is increased participation of renewables, increased investment in renewables, increased excitement about renewables."

Abbott's office and the United Nations did not immediately respond to requests for comment.

(Story refiles to correct headline to "PM" instead of "MP")

(Editing by Nick Macfie)