Some forecast models are showing the remnants of Tropical Cyclone Gita, which smashed through Tonga overnight, getting to New Zealand in about a week.
"There's still a risk it could come down and pass across New Zealand in just over a week's time but it's not something we have any definitive answer on just yet," MetService tropical cyclone forecaster Matthew Ford said.
"There's a spread of possibilities."
This evening, Gita is forecast to be hitting southern Fiji as a category 5 cyclone. Small islands expected to be most affected are Ono-i-lau and Vatoa.
About 5am local time (6am NZT) Fiji Meteorological Service said Gita was about 200km east-southeast of Ono-i-lau and moving west about 28kmh.
On that track, its centre was expected to be about 85km southwest of Ono-i-lau at 6pm NZT.
Winds were expected to increase to destructive hurricane force with average speeds of 195kmh and gusts to 275kmh.
Heavy rain and damaging sea swells were expected with sea flooding of coastal areas.
Close to the centre of the cyclone, average wind speeds of up to 195kmh were expected by 1pm, with momentary gusts to 295kmh.
Fiji Broadcasting Corporation (FBC) reported about 10 families on Ono-i-lau, which has five villages, had evacuated to higher ground.
Resident Kiri Verewale said people on the island were preparing for the worst, nailing boards on their windows for protection, and dismantling sheds.
People who lived near the coastline had moved to the local school and post office for shelter.
In the rest of the Southern Lau Group winds were expected to reach average speeds of 110kmh, gusting to 155kmh, also with damaging heavy swells and sea flooding of coastal areas.
FBC said schools in the Lau, Kadavu and Lomaiviti groups would be closed on Tuesday.
If the remnants of Gita do reach New Zealand in a week to 10 days, MetService's Ford said it was most likely the northern half of New Zealand would be affected.
"In a couple more day's time hopefully the models will have settled down and we will have a bit more of a consistent picture of what's going to happen."
WeatherWatch said computer models had been agreeing for days that Gita would swing out into the Tasman Sea then curve back around and make a direct hit into New Zealand.
It would be an ex-cyclone by then and it was unclear whether it would retain storm conditions, or just be a weaker area of low pressure.
It was also unclear which part of New Zealand it would come into, but that would most likely be in the west.
Models were still not in agreement about the timing of a potential landfall here, varying from late this coming weekend to mid-next week.