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MetService is forecasting snow as low as 400m about the ranges of Fiordland and Southland on Monday evening and early Tuesday morning.
A MetService spokesman said the snow would be brought by a front which is expected to move on to the far south of the South Island, from the southwest, during the day.
As well as snow, it was expected to bring rain to southwest parts of the South Island and some heavy falls in southern Fiordland.
Rainfall accumulations may approach warning amounts up to 90mm in Fiordland, south of George Sound, from Monday morning to early Tuesday morning.
Residents are advised to keep up to date with the latest forecasts in case a full warning, or other areas, are added, he said.