The rain is expected to turn to snow above 300m for those regions during Tuesday.
There was a moderate chance of the warning being upgraded to red.
Heavy rain could cause flooding, slips and difficult driving conditions.
A heavy rain watch is in place for Mt Taranaki, Westland District, Southland and Clutha about and northwest of Raes Junction on Monday. There was a moderate chance of these being upgraded to a warning.
But MetService said there was a high chance of the strong wind watches being upgraded to warnings for Westland (in place Tuesday morning to Wednesday noon) and The Fiords (in place Monday night to Wednesday morning).
These winds may approach severe gale in exposed places, MetService said.
And a snow watch will be in place for South Canterbury, including the foothills, inland areas of Otago and Southland as well as eastern Fiordland from Monday until Tuesday.
There was a moderate chance of the watch being upgraded to a warning, with snowfall possibly reaching warning criteria for the Otago, Southland and Fiordland areas.
“Snow level is expected to lower to 300 to 500 metres overnight Monday and during Tuesday morning with significant accumulations shifting towards eastern Otago.”
A road snowfall warning will be in place for Lindis Pass (State Highway 8), Crown Range Rd, and Milford Rd (State Highway 94), from Monday morning until night.
- RNZ