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It has also prompted a wry response from Director-general of Health Ashley Bloomfield at his 1pm press briefing today.
"Well he does get around, doesn't he?" Bloomfield said.
Mr Tamaki and wife Hannah left Auckland late on Saturday night and arrived in Rotorua about midnight, where they told a crowd gathered for the Sunday morning service they had escaped Auckland to avoid the Level 3 restrictions.
They have since been travelling down the country, and Mr Tamaki was seen in Te Anau on Tuesday.
When asked about the pair today, Dr Bloomfield said: "The request of them has been clear, they should be minimising their interaction with large groups of people."
On the potential damage of Hannah Tamaki saying she won't get the vaccine - reported earlier today - he said: "I'm confident we've got a really powerful narrative here, and NZers will take up the opportunity and make decision themselves."
Before Dr Bloomfield's response the travel had already copped some criticism from both locals and Covid-19 Response Minister Chris Hipkins.
A Te Anau resident was not happy seeing Mr Tamaki in town.
People in Te Anau believed they were relatively safe from Covid-19 as the town was so far away from any outbreaks, she said.
The visit from Mr Tamaki reinforced that it only took one visitor not following the rules to change that.
"It’s a conscious decision to flout the rules," she said.
"As a leader in the community he should be setting the example."
Fiordland Community Board chairwoman Sarah Greaney said many Te Anau businesses relied on Aucklanders being able to travel, and if they could not do so because people were being irresponsible, that had an impact.
"At the end of the day, people have to act responsibly."
"From a business perspective it’s incredibly frustrating," Ms Greaney said.
Mr Hipkins said yesterday the Tamakis’ actions were "completely irresponsible".
He encouraged everybody to exercise their own judgement.
"Sneaking out of Auckland right at the beginning of a lockdown and having large gatherings of people is simply putting people at risk unnecessarily."
At the Sunday service in Rotorua, Mr Tamaki, who describes himself as an apostle, explained his reasons for getting out of Auckland.
"We’re on lockdown three in Auckland, that means there’s to be no business for seven days.
"I made a decision with Hannah to go out before the 6am road blockages by the police...
"I’d be locked in my house. Gardening is OK, but I think I’ll be more productive out in the rest of the country."
He urged his followers not to fear the virus.
"God said that no plague will come near your house: ‘I will send angels to guard and look after those who are in the secret place with God’."
The Tamakis issued a strong response to the media attention they received for fleeing Auckland, saying it was "not the media’s job" to sanction them.
The NZ Transport Agency said about 9200 vehicles left Auckland from 9pm on Saturday to 6am on Sunday, far more than usual.
- Additional reporting RNZ/NZ Herald