She said tourists were still arriving on the island as recently as Sunday night.

"We don't know why because everything has closed down," she said. "The museum, the cultural centre, the golf course - there's nothing open for them to do anything.

"It makes us angry, and we don't understand why they're coming here. These people are endangering our lives as well as their own. They should be home."

On Wednesday morning Premier Peter Gutwein said anyone arriving on King or Flinders island must self-isolate for 14 days regardless of how much time they had spent on mainland Tasmania.

On Saturday, King Island mayor Julie Arnold encouraged visitation from Tasmania to the island to support businesses.

"Come and visit now, there's certainly no restrictions coming in," she said, in response to a question about whether Tasmanians should buy a ticket to King Island after the pandemic was over.

She has since claimed she was misrepresented.

She could not be reached for further comment.

Ms Munro said she believed the majority sentiment on the island was in favour of limiting movement on and off the island as much as possible.

"There are islanders over here - and I'm one of them - who have deferred medical treatment in Tasmania to protect our community," she said.

"No business is worth an islander's life.

"We have to protect our community more than anything in the world, because if we get one case of coronavirus on King island, it will wipe out half the population.

She said this was because the island has a small hospital and a high proportion of older people with underlying health conditions.

"We're scared," she said.

Rex airline will cease flights to and from King Island on April 6, but Sharp Airlines have not announced cancellations to either King or Flinders island, and there are also freight ships that travel between Tasmania and the islands.

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