Tropical Cyclone Ula is beginning its slow move towards the top of the North Island.

MetService meteorologist Claire Flynn said it's currently sitting between Fiji and Vanuatu, but the remnants of Ula will lie near New Zealand by midweek.

"There's a chance of heavy rain for Northern New Zealand on Tuesday, however, at this stage, we only have a low confidence associated with that because the track of the tropical cyclone gets much more uncertain as we get towards Tuesday and Wednesday."

Claire Flynn said at this stage they're expecting the cyclone to move southwards towards New Zealand, but then curve off to the southwest.

She said they're continuing to monitor the cyclone, which caused damage to Tuvalu and Tonga with high winds and heavy rain.