WeatherWatch said computer models showed the cyclone, which is currently a category three, was likely to drop to a category two before hitting New Zealand.
MetService said earlier it was expected to have become an ex-tropical cyclone.
At this stage both islands were at risk of flooding and wind damage on Tuesday and Wednesday. The upper South Island could also get very heavy rain.
MetService described it as "highly impactful severe weather".
Damaging winds could extend for hundreds of kilometres from the centre of Gita.
Models by the US Government's Joint Typhoon Warning Centre showed gales were possible from as far south as Dunedin to as far north as Taranaki, or even Waitomo and Central Plateau.
WeatherWatch warned that travel delays and cancellations were likely, including for those travelling by road, air and crossing Cook Strait, early to mid next week if Gita retained its strength.
MetService urged people to be prepared and check emergency kits had enough food, water, batteries and cellphone chargers.
WeatherWatch said it would likely be Monday before the precise area of landfall was certain. Cyclone Gita ravaged parts of Samoa, Tonga and southern Fiji this week and last weekend.
By the time the cyclone hit Tonga it was a category four and a state of emergency was declared. Aid and supplies have been sent to Tonga by the Defence Force.