The Greenpeace campaigners ascended the 70,000-tonne floating production unit at Woodside's Scarborough gas site off the coast of Western Australia early Saturday morning.
Activist Dr Chris Holden said the controversial project - set to produce its first liquid natural gas export by year's end - would irrevocably harm nature on Scott Reef, a coral atoll about 300 km off the Kimberley coast.
"With warnings like this from the leading global health professionals, our government simply can't allow fossil fuel projects like Woodside's Browse project to go ahead," Dr Holden said while carrying aboard a copy of the 2025 Lancet countdown report.
Once operational, the $18.6 billion project will provide up to eight million tonnes of LNG for export a year, as well as up to 225 terajoules of gas per day for domestic consumption.
But Greenpeace chief executive David Ritter said the Browse gas proposal would turn the Scott Reef into "an industrial gas zone".
"Greenpeace Australia Pacific is taking action today to expose the unacceptable risk to Scott Reef posed by Woodside's plans," he told reporters.
"Woodside wants to drill up to 57 toxic wells around Scott Reef, Australia's largest oceanic reef, home to nesting green sea turtles and endangered species like pygmy blue whales and the dusky sea snake.
"It is a place like nowhere else on Earth."
Mr Ritter said there was no future in new gas projects but rather "in secure homegrown renewable energy, green industry and exports".
"There's no future in dirty gas shipped offshore," he added.
The massive floating production unit arrived at the site 375km off Karratha in mid-January after being slowly towed from China - a voyage that took two months.
A 2021 report by the Conservation Council of WA and The Australia Institute warned Scarborough would produce an additional 1.6 billion tonnes of emissions, "equivalent to building 15 new coal power stations".
It said the project was the highest-polluting fossil fuel development proposed in Australia and would increase WA's total emissions almost five per cent or 4.4 million tonnes per year.
Woodside has insisted Scarborough has been subject to extensive review and will deliver one of the lowest-carbon LNG sources in Australia.
As of 11.30am local time, the company said it was still responding to an incident "involving individuals who have gained unlawful access to the Scarborough floating production unit".
"Our immediate focus is on managing the situation safely and minimising risk to the individuals involved and our workforce," a spokesperson told AAP.
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