More tornadoes like the deadly one that tore through a shopping mall on Tuesday are a possibility for the upper North Island today, forecasters have warned.

MetService says a severe thunderstorm will pass over the north and west of the North Island this morning, which will bring thundery showers and very strong winds.

"Right now the storm ticks all the boxes, and so tornadoes are a possibility among the thundery showers," MetService weather ambassador Bob McDavitt said.

"On Tuesday, the incoming thunderstorms didn't tick all the boxes. Whereas today, we've got another line of incoming thunderstorms and they are all ticking all the boxes for a tornado. So the potential is there to have one like Tuesday's."

A new low is forming in the Tasman Sea and over the next 36 hours will cover much of the country and eastern Tasman Sea.

Mr McDavitt said the "severe" thunderstorm could deliver up to 25ml of rain an hour, hail stones the size of 10c coins and 110km/h winds.

It was impossible to predict exactly when or where a tornado might strike because of the difficulty in forecasting which clouds would produce the spiralling winds, Mr McDavitt said.

"Tornadoes are so small and they last for such a short time that we don't get individual forecasts. The best that we can do is say here are thunderstorms, and one or two of them might produce a tornado. That's as close as we can get."

The tornadoes could be much smaller and less destructive than the one that tore through the North Shore this week.

"There might be tornadoes which will never be reported and will never be seen. They can form out at sea, or over farmland without anybody seeing them," he said.

Weather Watch chief analyst Philip Duncan said heavy showers and gales were possible during sudden bursts of rain.

"Conditions may be generally calm but with little warning, winds could rise to a damaging gale during squalls," he said.

Yesterday, Prime Minister John Key headed to areas on the North Shore that were worst hit by the tornado on Tuesday.

He spoke to Auckland Mayor Len Brown and the chief executive of Fletcher Building, who lost an employee, Benedict Dacayan, to the twister.

Mr Key visited Roseberry Ave in Birkenhead, a suburb south of Albany also hit by the tornado, and said it was incredibly isolated.

"It was obviously quite frightening for those involved and only the fourth tornado Auckland has had in 100 years, so it was a terrible natural event," he said.

Albany Westfield, which sustained minor structural damage to one wing, had 50 per cent of its stores open yesterday.

Ninety per cent of the nearby Albany Mega Centre was operating normally.

Demolition was continuing at Placemakers and the surrounding car park was closed. Farmers remains closed, but Pak 'n Save has reopened.

* Seek shelter in the lowest level of your home. Keep away from all windows.

* Cover your head and eyes with a blanket or jacket to protect against flying debris.

* Avoid large-span roof areas such as school gyms, shopping malls and halls.

* Crouch for protection beside a strong structure, or lie flat in low-lying area and cover your head and neck with your arms or a piece of clothing.

* Get out of the car and lie flat in a ditch or other low-lying area.