MetService says it has not seen a storm like Cyclone Cook since the one in 1968 that sunk the Wahine, killing 52 passengers.
A low-pressure system followed by the tail end of the cyclone is due to bring rain and gales to large parts of the country until Friday. A severe weather warning is in place.
The Thames-Coromandel District has declared a civil defence emergency ahead of the storm, and warned holidaymakers to stay away for the next few days.
In Bay of Plenty, a state of emergency extends from the Whakatāne District to the entire region.
The Ministry of Education advised 94 schools and 130 early learning centres to close tomorrow. The affected areas are: Eastern Bay of Plenty, Franklin, Great Barrier Island, Waiheke Island, Thames and Coromandel.
MetService warned some areas could experience up to 250mm of rain in the 48 hours from midday Wednesday, gusts of 150km/h or more, large waves in excess of 5m and storm surges.
Meteorologist Lisa Murray said on Wednesday the public was not taking the approaching storm seriously enough.
She said the whole of the North Island and much of the South Island would be affected.
Ms Murray said it was a deep tightly-packed low with possible gusts of 150km/h or more, and heavy downpours. She had worked at MetService for 12 years and never seen weather like this.
MetService said people should make efforts to stock up on supplies in the event of power cuts and road closures, avoid travel and stay up to date with warnings.
"People should be aware that this is a very significant event and is likely to produce widespread flooding, slips and wind damage, including to powerlines and may even lift roofs. Driving conditions are likely to be hazardous, so people will need to take extra care on the roads, and even consider altering their Easter travel plans."
It said the most intense weather was expected to hit land about 6pm on Thursday, but high winds and downpours would start earlier.
Heavy rain lashes Auckland
The bad weather begain in Auckland on Wednesday evening, with heavy rain causing flooding in at least 22 properties, including the Three Kings Plaza.
The NZ Transport Agency earlier said conditions on the roads and motorways in Auckland were very poor.
At Three Kings, a gym's delivery bay and a large area of its carpark was filled with knee-deep water.
City Fitness spokesperson Jackie Richards said it usually has more than 30 spaces available for cars but the flooding was taking up nearly half of them.
"Well at the moment we've got a reasonable-sized carpark but in one corner it is completely flooded.
"Any sort of heavy rain, yes, we will frequently see a small swimming pool."
She said the drainage system simply could not cope with large amounts of water.
Bay of Plenty
The state of emergency in the Whakatāne District was on Tuesday extended to the entire Bay of Plenty, which was forecast to get up to 250mm before the end of Thursday.
The Bay of Plenty Regional Council said the stopbanks along the Rangitāiki River, which burst in last week's torrential rain, flooding Edgecumbe, were likely to hold in the latest onslaught, but it could not be absolutely certain.
RNZ's reporter in the area said residents were on standby to evacuate if needed.
Strong winds were forecast from Auckland through Bay of Plenty and as far south as Wellington from Thursday.
In Bay of Plenty and Waikato, farmers were being urged to move stock to higher ground.
Thames-Coromandel mayor Sandra Goudie said the high likelihood the storm would hit the Coromandel Peninsula, bringing heavy rain on Thursday, was a major concern.
Some residents living in low-lying coastal areas might need to be evacuated, she said.
Ms Goudie warned any holidaymakers to stay away from the Coromandel area until at least Saturday - or potentially face closed roads and being cut off.
Thames-Coromandel Civil Defence Controller Gary Towler confirmed that advice.
"It is too dangerous, we really don't want you to come on the peninsula until at least - you know, we assess the weather - maybe late Friday.
"But certainly through this near period of Thursday through Thursday night we're just recommending people just stay away."
In Dunedin, the city council was preparing sandbangs in Opoho, Mosgiel, Ocean View and South Dunedin, and had set up evacuation centres in case of heavy rainfall.
Civil defence controller Ruth Stokes said on Wednesday trhat evacuation centres would be set up in South Dunedin, North Dunedin and Mosgiel, but locations had not been finalised.
She said council contractors had been clearing mud tanks and gutters as well as two minor slips on Portobello Road.
All sportsgrounds and freedom camping sites were closed and there would be no rubbish collection for the CBD, Mosgiel or South Dunedin on Thursday, she said.