MetService also said there was a "low confidence" it would bring warning amounts of rain.
And campers were advised to hold out hope - as there was a chance the storm would sweep past the country.
"The computer models are showing the centre of the storm weakening and pulling away to the south east, offshore to New Zealand's east coast," WeatherWatch said.
"But, as with any cyclone in our neighbourhood, there's always the chance it may 'wobble' a little in its path, and that could mean some chance it moves a little closer to land."
And it could be good news for surfers, as WeatherWatch said even if the storm remains offshore there would be a chance of large swells.
"But deep offshore lows can bring in dangerous rips and currents, even if the weather is sunny on the beach, something particularly important to note with so many families on holiday."
It said the chance of a "direct hit" from Cyclone Ula was low, based on its latest weather modelling, adding: "Generally speaking, it's not looking too concerning."
But even if Cyclone Ula skips past relatively unnoticed, the North Island is in for rain in the coming week.
Tuesday showed the chance of rain across northern parts, but a large high would roll back in bringing mainly dry, settled weather across the country, Weather Watch said.
MetService warned a front is expected to move northeast over the south of the South Island late on Tuesday and during Wednesday morning, with the possibility of warning amounts of rain in Fiordland.
Main centres forecast
•Whangarei: Sunday will see cloudy periods, a chance of a shower, and a high of 24C. Cloudy periods on Monday, the odd shower, easterlies and a high of 23C.
•Auckland: Cloudy periods today, with a shower or two and southwesterlies, a high of 22. Monday will be fine, with a few afternoon showers in the west, with easterlies and a high of 24C.
•Hamilton: Cloudy periods, with the chance of a shower today, a high of 23C. Fine spells on Monday, and the chance of an afternoon showers, light winds and a high of 22C.
•Tauranga: A chance of a morning shower on Sunday, then fine, with westerlies and a high of 25C. Cloudy periods and a few showers on Monday, a northeast develops, and a high of 21C.
•Wellington: Cloud increasing on Sunday, with the chance of showers, a strong northerly changes to a southerly, with a high of 23C. Tomorrow will be fine apart from evening cloud, northerlies develop, and a high of 20C.
•Christchurch: Sunday will see cloudy periods, a chance of morning showers, and a strong southerly change, with a high of 19C. Monday will become fine in the morning, a developing northeasterly, and a high of 19C.
•Dunedin: A few showers today, clearing in the afternoon, a gale southeast easing, with a high of 19C. Fine on Monday, with developing northeasterlies and a high of 18C.