As Pacific leaders gather in Fiji for the Pacific Islands Forum (PIF) this week, Vanuatu is spearheading a campaign to seek an advisory opinion from the court.
The Melanesian state wants the ICJ to consider whether international law requires countries to meet their emissions-reduction targets to protect the human rights of future generations.
The matter is bound for a vote of the United Nations General Assembly later this year, requiring a majority to pass.
Climate campaigners believe such an opinion would strengthen demands on wealthy and high-emitting nations to cut their greenhouse gas use and reduce future warming.
Speaking on the eve of the leaders' summit, Jacinda Ardern signed New Zealand up.
"We're supportive of those moves," Ms Ardern said.
"We haven't got to the stage yet of whether there's any particular wording or framing for that, of course we'd want to make sure that we're able to sight that, but as a general principle we're supportive.
"This would be one of a number of measures that ... those who are most climate-affected are seeking to take to ensure that those who have the greatest power and the largest impact on climate emissions reduction, (to) make sure that they are doing their bit."
Australia - which has lifted its emissions targets under Anthony Albanese's government - has joined the chorus of support.
Pacific Minister Pat Conroy suggested Australia would also vote in favour.
"We are supportive of the process," Conroy said. "And we applaud Vanuatu taking it to the UN General Assembly.
"This is a really important resolution that will help increase momentum for action on climate change."
While other issues are swirling - not least regional unity in the wake of Kiribati's withdrawal from the forum - climate change remains at the forefront of the PIF agenda.
Global warming is an existential threat to several low-lying Pacific countries, and, if unchecked, will cause major ecological and economic damage to the developing region.
Officials in Suva say Mr Albanese's election on a climate platform was promising.
"They're saying the right things," one told AAP, "and now ... everyone is waiting to see whether there's follow-through."
Speaking at an event in Sydney prior to his departure for Fiji, Mr Albanese said he wanted Australia to "be a trusted global partner on climate action".
Australia is also gunning to host a first UN climate summit on behalf of the Pacific, "to elevate and prioritise issues which impact our region the most".
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