Wellington mayor Andy Foster believes residents shouldn't panic as the region's first positive Covid-19 case in weeks is confirmed.

The Ministry of Health said today a person in Wellington who had returned a weak positive test result yesterday, had recorded a second positive result today - confirming them as a positive case.

Yesterday, Wellington Water acting chief executive Kevin Loke told the NZ Herald the case was a staffer working on the Omāroro reservoir construction site in Mt Cook.

"The site is open air, has been complying with Covid-19 protocols and has kept a record of everybody who has been on site. We are following the advice coming from the Ministry of Health as we respond to this situation," he said.

The initial positive test result was picked up as part of routine surveillance testing.

Investigations have identified a small number of close contacts, including the person's co-workers, who are currently isolating and being tested. All results have come back negative so far.

It is understood the person, who had come from Auckland as an essential worker, is double-vaccinated and an active user of the Covid tracer app.

A central Wellington supermarket was released as a location of interest - Countdown Cable Car Lane on Lambton Quay on Tuesday between 7.12pm-7.30pm.

Foster acknowledged the location was very central but was glad the visit was fleeting, with just 18 minutes of exposure.

He pointed to the negative test results from co-workers as a good sign.

"I think the risk looks like it should be pretty low because the workmates on the site have all been tested and my understanding is they've all come back negative.

"I think people should feel as though they can go about their normal lives but keep on doing the things that we do... mask-wearing, contact tracing, and if you're not feeling well, get yourself checked out."

Public health staff had not yet informed him on the risk level of the case.

Wellington recently hit 90 per cent fully vaccination among residents, which Foster cited as proof Wellingtonians were prepared for any rise in cases.

"Obviously, the level of vaccination is really, really fantastic, particularly in Wellington City, so keep doing the right things and keep getting ourselves prepared because we know when the Auckland border opens, we are going to see cases spread throughout the country."

The ministry is urging anyone in Wellington with Covid-19 symptoms to get tested, even those who are vaccinated.