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On Saturday the minister signed a commitment to rid the island of pests with groups including councils and iwi.
Ms Sage said the "ambitious vision'' to back nature on the island would make it the "largest inhabited predator-free island in the world''.
Predator Free Rakiura aims to remove rats, possums, feral cats and hedgehogs from the mainland and islands of Rakiura.
The islands are already free of stoats, weasels, ferrets, pigs and goats.
The islands are home to unique endemic plants and wildlife like the endangered Rakiura tokoeka kiwi, the Stewart Island robin, and harlequin gecko, which are not found anywhere else.
Ms Sage said it was "an exciting step forward for both the local Rakiura/Stewart Island community and conservation across Aotearoa''.
"As such, it is a significant project in the national Predator Free 2050 goal. Rakiura/Stewart Island is home to many threatened species whose ongoing survival globally depends on conservation right here.''
She described the move as "significant''.
Funding from the latest budget allowed for predator control totalling $81.2million over four years, and enabled the Department of Conservation to scale up its response to the biggest mast event (a prolific beech tree flowering, with associated predator boom) in 40 years.