Meteorologist Rob Kerr said the South Island would enjoy better conditions, particularly for the ski fields.
"Conditions should be great outdoors until the winds strengthen late in the week," Mr Kerr said.
WeatherWatch head weather analyst Philip Duncan said the north could experience wind gusts of more than 120km/h by tomorrow evening, particularly in northern and northeastern areas.
"On top of the recent heavy rains in northern New Zealand the soil is saturated and strong to gale force winds may topple trees easier," Mr Duncan said. "This may also lead to further isolated power cuts and hot water cuts."
Eastern Waikato and Coromandel Peninsula may also experience damaging gusts overnight Tuesday and Wednesday, with the potential for power cuts.