Desires for retribution must be quelled to ensure the country gets through the Covid-19 pandemic, political leaders say.
The Government says police will join health authorities when needed to keep tabs on people supposed to be self-isolating.
A capability to prosecute people for lockdown breaches has already been established, with 629 prosecutions pursued during level 4 last year.
But Act leader David Seymour said better monitoring of people supposed to be self-isolating had greater benefits than a punitive, reactive approach.
Auckland's descent into a fourth lockdown showed New Zealand was losing its lustre as a global leader in the fight against coronavirus, Seymour said.
A 21-year-old man who went to a gym after getting a Covid test, before receiving a test result, has caused widespread frustration in South Auckland and beyond.
Seymour said people might have strong instincts for retribution against those seen to have endangered the community.
But he said calls to harshly punish those who breached Covid protocols could lead to people being penalised for innocent mistakes.
Errors could be prevented with a proactive approach better designed to prevent disastrous breaches, Seymour said.
He said Taiwan used triangulation of cellphone towers to track people's locations and frequently ensure compliance with stay-at-home orders.
The Taiwan system has been called a "carrot-and-stick" approach.
It at one point included fines exceeding NZ$49,000 for people who stepped outside during quarantine, but rewards for those who complied.
"Part of the difference is, we're relying on 100 per cent honesty with practically no enforcement," Seymour said.
"But if you punish people severely, then you erode trust."
Seymour said the outbreak showed improvement was needed and the Government still had time to change aspects of New Zealand's Covid-19 response.
"They can no longer claim that we're somehow different or better than the rest of the world."
More investment was needed for a likely future pandemic, Seymour said.
"I suspect this won't be the last one in my lifetime or the near future."
He said Taiwan's success stemmed largely from lessons learned and investments made after the early 2000s Sars pandemic.
National Party leader Judith Collins told TVNZ's Q+A police should be dispatched if people in isolation did not respond to Government messages within 24 hours.
Under the Health Act, police may use force to ensure compliance with a medical officer of health's requirements, such as self-isolation.
Prime Minister Jacinda Ardern said police would join health authorities if it was suspected people were not self-isolating.
She told a press conference today most people did already respond to messages and checked in when required during self-isolation.
"What we have here are a handful of cases where they haven't, and it has had dire consequences.
"What we will be doing is enabling health of course to work with police when they have concerns that someone is not following the rules, to have a check-in in place.
"We try to leave as little excuse as possible for not hearing the message that we are at level 3 in Auckland," Ardern added.
She said despite the country's efforts, some recent cases had gone to work when they should not have.
"When you get a test, you must isolate at home until you've received a negative test result," Ardern said.
She said financial support was available during the pandemic, including the Short-Term Absence Payment for people unable to work while waiting for test results.
Ardern and Health Minister Chris Hipkins both expressed annoyance at the latest case but urged against demonising the man known as Case M.
The new South Auckland cases led community leaders there to voice irritation, but to also call for unity.
Case M spent four hours working as a casual contractor at Kerry Logistics Oceania in South Auckland early last week.
Kerry Logistics managing director Rob Gilhooly said the case was frustrating.
"We've taken all the precautions. The facility has been deep-cleaned today."
He said Case M arrived on site through an external labour hire company.
The labour company said the man visited Kerry Logistics on Tuesday, and details of Case M's contacts were supplied to the Ministry of Health as requested.
Auckland is expected to stay in level 3 until 6am on Sunday, March 7.