MetService meteorologist Amy Rossiter described the storm as "very fast moving".
"There's a bit of uncertainty around the track it will take," she said.
"Currently we're expecting it will touch on shore from Northland to the East Cape."
MetService was warning of heavy rain, surface flooding and slips in those areas.
Strong winds were also expected for Northland, Great Barrier Island, the Coromandel and Auckland, as well as further south in the Bay of Plenty and Gisborne.
The New Zealand Red Cross was urging Kiwis to prepare for the worst, by stocking up on food and locating the first aid kit.
The centre of the storm was sitting to the East of Norfolk Island this morning, where it was expected to create 7m-high swells.
It was expected to remain a category 2 until about midnight tonight, when it would be downgraded to a category 1 storm.
At this point, its classification would change from being a tropical cyclone, to an ex tropical cyclone.
MetService would continue to issue updates as the cyclone's path becomes clearer.
It is warning that significant damage and disruption is possible, including downed power lines, flooding, slips and damage across roads, and large waves affecting low-lying coastal areas.
Those in the upper North Island were being urged to use yesterday's relative calm to prepare for the storm damage.
Northland, Auckland, Coromandel Peninsula, Waikato, Bay of Plenty and Gisborne are all expected to get at least some of the severe weather on Monday.
It is likely the heavy rain and gales will hit Waitomo and Taranaki across to Hawke's Bay later on Monday and into early Tuesday.
It is unlikely to go as far south as Wairarapa.
The tropical cyclone has battered Vanuatu with winds of up to 230km/h and left the small Island country in cleanup mode.
The roof of a classroom was blown off and some houses collapsed in Vanuatu. There was also one death from a falling tree reported.
More recently, New Caledonia escaped the worst of the deluge.
Authorities had lifted all cyclone alerts for the country yesterday, though people were being warned some travel disruptions could continue.
