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Flights from Christchurch, Blenheim, Auckland, Tauranga, Timaru, Rotorua and Nelson between 6.30am and 8.20am have been cancelled, Air New Zealand's website says.
No reason has yet been given for the cancellations but the Herald understands it is weather-related.
A severe weather warning has been issued for parts of New Zealand, with gales gusting up to 140kmh in exposed areas.
Air New Zealand has been contacted for comment.
MetService meteorologist Lewis Ferris said the rain will be the "most impactful" on Tuesday, and will lash the West Coast of the South Island all week.
"We're likely to see over 500mm of rain in the West Coast of the South Island," he said.
Strong northwesterly winds are expected to accompany the heavy rain and blow around the centre of the country and eastern areas of the South Island, he said.
Thunderstorms are likely to hit the area on Tuesday and slips, while flooding and road closures are possible.
Aucklanders will likely see a less dramatic smattering of rain on Tuesday, with a burst of rain and a chance of thunder forecasted in the City of Sails in the afternoon.
But the temperatures are expected to stay warm in the city, with expected highs upwards of 24C and warm overnight temperatures this week.
It's a similar story in the Bay of Plenty, with the chance of a few showers on Tuesday, northwesterly winds and balmy temperatures.
Napier is in for a scorching few days, reaching a high of 29C on Tuesday and soaring up to 31 on Thursday.
And it won't cool down overnight, with expected temperatures on Monday evening to shoot 8C higher than the normal recorded overnight temperature during December.
Wellington's in for a windy week, where a severe weather warning for gales has been issued.
Ferris said gales could gust up to 140km/h in exposed places, but the temperatures are expected to remain warm.
Christchurch won't be affected largely by the West Coast rain, and will see cloudy and warm weather with northwesterly winds and temperatures spiking above 25C.
Dunedin will be a few degrees cooler than Christchurch in the next few days, and will see a bit of rain, Ferris said.
Rain will also hit Invercargill this week, but temperatures are expected to hit the 20C mark or a few notches below.