The high school at the centre of the cluster that has sent New Zealand's biggest city into two lockdowns has been subjected to abuse - including one email so bad, it had been referred to police.

Papatoetoe High School principal Vaughan Couillault says although the school was mostly receiving positive feedback there had been negative comments on social media.

Couillault told Newstalk ZB's Mike Hosking today that by tomorrow everyone at his school would have either been tested twice or spent a fortnight in self-isolation.

"We're getting some emails - I got a few yesterday - things like 'sort your lot out, your kids are a disaster, your school's a joke, you're a joke', all that sort of stuff that you can quite easily say when you're anonymous and behind a keyboard," said Couillault.

"I did pass one on to the police because there was a bit of vitriol in it with words that would have offended my mother," he said. "My mother's not easily offended, I might add."

However police told him there was not much they could do as there was no tangible threat, he said.

However, they did follow it up to make sure it wasn't anything more sinister.

Couillault said he was looking forward to the alert level being lowered and school resuming.