The federal government's final tick of approval for Australia's biggest gas project to continue operating until 2070 may have breached the environment minister's international legal obligations, a traditional owner says.

Environment Minister Murray Watt green-lit the 40-year extension for Woodside Energy's controversial North West Shelf development in Western Australia's Pilbara region on Friday.

Murujuga traditional owner and Mardathoonera woman Raelene Cooper said the decision was "a slap in the face" and "a crime against humanity".

"This is not just destroying Murujuga country, but will impact communities all around the world," she said.

"It is a betrayal of Aboriginal people, it is a betrayal of our Elders, it is a betrayal of future generations. It is a betrayal of all Australians

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