Uncle Paul Kabai and Uncle Pabai Pabai first launched the Federal Court proceedings in 2021, fearing for their homes on Saibai and Boigu islands.
They sought orders that would require the government to take steps to prevent harm to their communities, including cutting greenhouse gas emissions in line with the best available science.
Federal Court Judge Michael Wigney in July 2025 accepted key facts of the case, including that scientific evidence showed climate change had already impacted the Torres Strait.
But he ultimately ruled against the elders, finding negligence law did not allow for compensation when it came to government policy decisions.
The uncles are challenging Judge Wigney's decision, with a four-day appeal hearing set to start in Melbourne on Tuesday.
Their legal team will argue the judge made errors in his legal conclusions and the Commonwealth does owe a duty of care to Torres Strait Islanders.
They will also contend the Commonwealth's additional emissions are a legal cause of harm and cultural harm is compensable under Australian law.
Uncle Paul, who will attend the hearing on Tuesday, questioned why the federal government was turning a blind eye to those Indigenous people who were experiencing climate change.
"Where's the duty of care for people affected by rising sea levels, bushfires and unpredictable storms?" he said in a statement.
"Why is it the people who don't contribute much to climate change are the ones most affected?
"We Torres Strait Islanders will be the first climate change refugees."
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, Climate Change Minister Chris Bowen and Indigenous Australians Minister Malarndirri McCarthy said the government understood the Torres Strait Islands were vulnerable to climate change and were already feeling its impacts.
"Where the former government failed on climate change, the Albanese government is delivering - because it's in the interest of all Australians," they said in a joint statement.
In September, the Albanese government set a target to reduce greenhouse gas emissions between 62 to 70 per cent compared to 2005 levels by 2035.
Chief Justice Debra Mortimer, Justice Craig Colvin and Justice Nicholas Owens will preside over the four-day hearing before delivering a judgment at a later date.