Scattered through the warm waters off Australia's northernmost tip, the sparsely populated Torres Strait Islands are threatened by seas rising much faster than the global average.

Torres Strait elders have spent the past four years fighting through the courts to prove the government failed to protect them through meaningful climate action.

Australia's Federal Court found the government was not obliged to shield the Torres Strait Islands from climate change.

"I thought that the decision would be in our favour, and I'm in shock," said Torres Strait Islander Paul Kabai, who helped to bring the case.

"What do any of us say to our families now?"

Federal Court Justice Michael Wigney criticised the government for setting emissions targets between 2015 and 2021 that failed to consider the "best available science".

But these targets would have had little impact on global temperature rise, he found.

"Any additional greenhouse gases that might have been released by Australia as a result of low emissions targets would have caused no more than an almost immeasurable increase in global average temperatures," Wigney said.