Antonio Guterres attended a community roundtable event in Auckland Monday, as he kicked off his Pacific tour.
He departs for Fiji on Tuesday before heading to Tuvalu and Vanuatu to complete his regional tour.
Mr Guterres said the Pacific islands were the first victims of climate change.
"Not only some of them because of the rising level of water represents an existential threat, some might disappear, but also because of course climate change brings with it a lot of negative consequences," he said.