Invercargill Mayor Tim Shadbolt says Brian and Hannah Tamaki are not welcome there, after the couple fled Auckland's lockdown on the weekend.
On Saturday night, Prime Minister Jacinda Ardern announced Auckland would enter Alert level 3 at 6am the next morning.
At the same time, the Tamakis packed their bags to leave for Rotorua before the curfew began.
They have since travelled to the South Island with plans to visit Invercargill, something which has not pleased the town's mayor.
"I find it exasperating that anyone would flee a Level 3 region and willfully joyride through other cities with such a reckless disregard for public health and safety," Shadbolt says.
"The people of Invercargill have stood and obeyed the rules for the benefit of the team of five million. We don't welcome anyone to our community who selfishly makes the choice to actively put others at risk.
"The concept of five million Kiwis all aboard the same waka will only work if we ALL agree to get aboard. It's very simple. Climb up and join the team or don't come South."
Director-General of Health Dr Ashley Bloomfield was asked about the couple by reporters at today’s 1pm briefing: firstly, whether he knew that Destiny Church leader Brian Tamaki has now been spotted in the South Island after leaving Auckland shortly before the Alert Level 3 lockdown came into effect.
“He does get around, doesn’t he. Goodness,” Bloomfield said.
“There was a lot of travel from people out of Auckland to the rest of the country and that’s why we are using Alert Level 2 in the rest of the country.
"Whether it’s the Tamakis or anyone out of Auckland, the request of them has been clear that they should be minimising their interaction with large groups of people.
"In fact, there should not be large gatherings anywhere in the country because of the alert level restrictions."
He was then asked how damaging it was that Hannah Tamaki has stated she will not have a Covid-19 vaccine just before the Government's messaging around it is due to come out.
"Here is someone who has clearly stated their intention not to get the vaccine and they may change their mind, but there are also many New Zealanders who have stated their intention to get the vaccine and I am one of them," Bloomfield said.
He added that he's "confident in our narrative" around the vaccine rollout messaging to the public.