Northland, Auckland, Bay of Plenty and Coromandel have the greatest odds of heavy rainfall, NIWA says.
NIWA meteorologist Chris Brandolino said a low pressure would form south-east of New Caledonia in the next day or so.
That would track south, probably to the west of New Zealand.
"It'll siphon down this really rich tropical air from the north and that will be the fuel for rain," he said.
The system would also bring gusty, strong winds, making it "pretty breezy" across the upper North Island, especially Northland, from Saturday afternoon.
On Sunday, rain would unfold across Northland - with some possibly heavy local falls - and into the Auckland area and Coromandel.
"At the moment it looks like this initial round of rain shouldn't be too problematic but whenever we have air coming from the tropics it raises awareness that there could be heavy rain locally.
"Pinpointing that now is a bit too far away."
Once that low shifts off to the south and south-west it will give the west of the South Island a good drop of rain early next week.
The tropical air stream will bring sultry weather to the country early next week, with bouts of rain, especially in Coromandel, Bay of Plenty and the upper North IsLnd
The west of the South Island will get a "good drop" of rain early next week, once the low shifts off to the south and south-west.
The more intense and widespread surge of heavy rain was likely later in the week, he said.
From the middle of the week the winds from the north and east will increase and that will be associated with another round of rain.
Coromandel, Bay of Plenty, Auckland and Northland would once again see heavy rain in the later part of the week.
RNZ
