Community leaders Uncle Paul Kabai and Uncle Pabai Pabai first launched Federal Court proceedings in 2021, fearing for their homes on Saibai and Boigu islands.
They sought orders requiring the government to take steps to prevent harm to their communities, including cutting greenhouse gas emissions in line with the best available science.
In July 2025, Federal Court Justice Michael Wigney accepted key facts of the case, including that scientific evidence showed climate change had already impacted the Torres Strait, north of Cape York.
But he ultimately ruled against the Elders, finding negligence law did not allow for compensation when it came to government policy decisions.
The duo have challenged Justice Wigney's decision in a four-day appeal hearing that began in Melbourne on Tuesday.
Outside the court, Uncle Pabai said it was a very important battle for Torres Strait Islanders after their initial defeat.
"We've been here before, this is our second journey to the Federal Court," he told AAP.
The government should be consulting with Torres Strait Islanders about climate change impacts as they tried to find a way to continue cultural traditions, Uncle Pabai added.
"We don't want to be climate change refugees relocated from our islands."
His legal team argued Justice Wigney made a number of errors in reaching the conclusion that the Commonwealth did not owe a duty of care to the islanders.
One was his ruling that setting national emissions targets was a core government policy decision that, due to the separation of powers, lay outside of the court's remit.
The Elders' barrister Fiona McLeod accepted that committing to the Paris Agreement - which outlines a 1.5C temperature-rise target - was a policy decision.
But she argued the government then set "an unambitious and unfair target which contributed to the whole of the problem worsening with local impacts".
It did not take the action reasonably required to protect a community it knew was vulnerable to the effects of climate change, Ms McLeod told the court.
"By stepping into the field, you have assumed a responsibility ... in doing so, the acts you are undertaking have to be done mindfully of those who might be harmed by your actions," she said.
"A government can't avoid a recognition of duty of care in all cases by simply classing them as a group of policies such as climate change that are no-go zones or subject to some sort of immunity."
Among the six grounds of appeal is an argument that cultural harm is compensable under Australian law as a loss of rights warranting protection and remedy.
Aunty McRose Elu, a Saibai Elder, said the situation in the Torres Strait was getting more severe and yet there was still no action.
"The time is getting closer (when) the islands will go underwater," she said in a statement.
"We can change. And if we don't take action now it will be too late."
Following the 2025 decision, federal Labor ministers said they understood the Torres Strait Islands were vulnerable to climate change and were already feeling its impacts.
In September, the Albanese government set a legislated target to reduce greenhouse gas emissions by 62 to 70 per cent by 2035, based on 2005 levels.
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