Meanwhile lifeguards are warning beachgoers to take extra care, with large, unpredictable waves and strong rip currents expected in popular holiday swim spots as soon as tomorrow ahead of Cody's arrival.
MetService said a large ridge of high pressure was spreading northeast across the country today and would persist through to Saturday, bringing mostly settled weather.
Cyclone Cody was expected to approach the waters northeast of New Zealand this weekend, MetService said on Thursday afternoon.
The current forecast showed it moving south to affect mainly the eastern North Island from late Sunday through to Monday, "possibly bringing significant impacts to these areas" - but there was still uncertainty regarding its movement.
The heavy swells were one of the earliest indicators that Cyclone Cody was on its way, MetService said. Potentially flooding rain and damaging wind would arrive early next week.
Cyclone Cody entered the MetService area of responsibility as it crossed a latitude line of 25S this morning - previously it was the responsibility of the Fiji Meteorological Service.
Before leaving Fiji the then-category 1 storm left one person dead, caused widespread flooding and forced close to 2000 people to flee their homes.
MetService meteorologist Raveen Das told Newstalk ZB this morning the cyclone's track was being closely monitored and where it made landfall could change.
The system would lose its tropical cyclone characteristics before arriving here but would still maintain its momentum - with the same windspeed and potential heavy rain.
"We are still taking it very seriously," he said.
MetService has since tweeted that "5-8m waves with long period swell from the east has potential for significant impacts about the coast", while Gisborne has been warned it's at high risk of heavy rain.
Heavy rain - over 25mm per hour - and severe gales were highly likely in Gisborne from late Sunday into Monday, while there was moderate confidence of warning levels of rain and severe gales in exposed places for Great Barrier Island, Coromandel Peninsula, Bay of Plenty and Hawke's Bay, MetService said.
Northland, Auckland, Waikato, parts of the central high country, Wairarapa and the Kaikoura Coast and Ranges, also had a possibility of warning amounts of rain on Monday and severe gale winds.
'In addition to heavy rain and strong winds, Cyclone Cody is expected to bring significant easterly swells, sea surges [and] rips and coastal inundation to the east coast areas from Saturday onwards," MetService said.
Surf Life Saving New Zealand national search and rescue manager Allan Mundy has warned the conditions created by Cody were likely to pose great risk to swimmers and other people in coastal areas.
"They create strong rip currents, strong winds and large surging waves inundating the beach, which are a hazard for would-be swimmers and walkers alike."
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All eastern North Island beaches are expected to be impacted to some extent, including those in Northland, Auckland, Coromandel, the Bay of Plenty, Gisborne and possibly Hawke's Bay. Civil Defence teams along the coast are on standby.
Niwa said this morning modelling showed there would likely be "significant impacts" in parts of New Zealand.
"This includes heavy rain, damaging winds and large waves," Niwa said. "However, the exact track will determine where the worst impacts occur, which remains uncertain."
TairÄwhiti Civil Defence said yesterday the cyclone was predicted to arrive in the region late on Sunday.
Campers and people living in coastal communities were warned there could be heavy swells up to 6m high, as well as heavy rain that could affect roads and inland areas.
Those in coastal locations and areas that have previously been prone to flooding should be keeping an eye on MetService updates, Civil Defence said.
Further north, Thames Coromandel District Council warned that the Coromandel area was in line for "huge surf and wind" at a minimum - regardless of where the storm headed.
Wave heights next Monday could reach 5m with wind gusts of 25 knots.
"If the system comes close there is the potential for flooding, rain, damaging winds and coastal inundation," MetService warned.
The council would be activating its emergency management team today and would be making people aware if they could be affected when Cody hit.