Cyclone Cody is set to track far east of the East Cape tomorrow, and MetService is advising the risk of heavy rain has diminished.
But it warns people in exposed parts of eastern Bay of Plenty and Gisborne should still be aware of a risk of severe gales.
It expects hazardous conditions in exposed eastern coastlines of the North Island, with large swells, significant sea surges, rips and coastal inundation possible.
That is separate from any tsunami risks from the Tonga volcano although MetService said people should be alert for high waves over the coming days.
Its aviation team has been issuing advisories to ensure no planes fly through the cloud of volcanic ash from the eruption yesterday of the underwater volcano Hunga-Tonga-Hunga-Ha'apai.
MetService said Cyclone Cody is currently over waters to the northeast of New Zealand, is expected to move southwards and pass far to the east of East Cape tomorrow, and then track south towards the Chatham Islands on Tuesday.
Head of weather communication Lisa Murray said: "Wave buoys have already recorded large waves for northeastern coasts. These are separate to the tsunami wave from the Hunga-Tonga- Hunga-Ha'apai volcano which has affected parts of New Zealand.
"We are advising people to be on alert for high waves over the coming days.
"Waves of this size and direction mean that they will be seen in places that rarely see large waves and are usually considered safe for swimming, so please take care."
MetService is also the volcanic ash advisory centre for Tonga's volcano so its aviation team has been ensuring no one flies through the cloud of ash thrown up in yesterday's eruption.
"We are also providing forecasts to the Ministry of Foreign Affairs and Trade in support of the relief effort."
- RNZ
Motorists are being warned to expect hazardous driving conditions.