The island will be directly hit by Cook later on Monday and into Tuesday before the cyclone turns towards New Zealand.
Vanuatu has already been hit by considerable flooding over the past day.
More flooding rains were possible next week in New Zealand especially towards Thursday and Good Friday, Duncan said.
"When we think of cyclones we tend to think of major wind and rain events, however by the time they reach New Zealand more often than not it's the rain that causes the bulk of the issues," Duncan said.
"Cook is not a very big cyclone size-wise - but it has a huge amount of moisture wrapped around it."
Later next week Cook's rain belt will connect with a sizeable low in the Tasman Sea pulling in very heavy rains which will be heavy enough to cause further serious flooding in New Zealand.
In Edgecumbe, 1600 residents have been displaced by the breaching of a floodwall on the Rangitaiki River.
The Edgecumbe township remains largely cordoned off to ensure public safety while floodwaters are still being managed and pumped away, and to protect people from sanitation risks associated with sewage system failures and surface water contamination.
"The past few days the forecast models have shown a similar trend of heavy rain in the Edgecumbe and eastern Bay of Plenty area," Duncan said.
"However a few more days are yet to go by before we can clearly see who will be impacted by this system, or if it might even slip closely past us without issues."
On the positive side, Cook appeared smaller and faster moving than Debbie, but Duncan still recommended those in flood-prone areas keep an eye on developments.
Monday's forecast:
Northland Cloudy periods, with a few showers.
Auckland and Coromandel Peninsula Fine spells and the odd shower, mainly in the north and east. Showers increasing about Coromandel Peninsula tomorrow.
Waikato to Wellington Mostly fine, however cloudy periods and the odd shower about and north of Taupo tomorrow.
Gisborne and Hawke's Bay Cloudy periods. A few showers about Gisborne spreading elsewhere for a time tonight and in the morning.
Nelson, Marlborough and Canterbury Generally fine weather.
Buller, Westland and Fiordland Fine today. Cloudy tomorrow, with rain developing south of Hokitika late morning, then retreating to Fiordland in the afternoon.
Otago and Southland Fine today. Scattered rain from tomorrow afternoon.