Mayor Julie Arnold said the current business support package put forward by the Tasmanian government wouldn't touch the sides for many businesses impacted on the island, and expressed serious disappointment in the messaging advising visitors to stay away early into their recent COVID-19 outbreak.

"I don't know anywhere else in Tasmania that was named and shamed like we were," Cr Arnold said. "They closed us, and then when they opened us up they just brushed it off."

On January 6, Public Health requested those planning to travel to the island reconsider the necessity of their trip. This recommendation was withdrawn on January 14, once it was deemed the outbreak had passed its peak.

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Cr Arnold said while operators were looking at the small business grants on offer, the amounts available were minor considering the losses that had been taken.

"I would have hoped there would be a package which actually took into account the substantial damage done to us by the suggestion that people not travel.

"People were booked out until March.

"...They had less than three weeks and it fell in a heap again."

Cr Arnold said the island was still hopeful some of the damage could be overturned with a few months of the peak visiting season still to come, and operators eager to welcome guests.

"We're doing everything that we should, and we're hopeful our tourism industry might still have a chance."

Health Minister Jeremy Rockliff said the government had "followed Public Health advice at every step and (would) continue to do so as the situation continues to develop".

"The new COVID-19 Business Impact Support Program which opens on Wednesday 19 January is designed to help these businesses get back on their feet," Mr Rockliff said.

"Through Tourism Tasmania, the government will also work closely with King Island tourism organisations and operators to promote the Island through its marketing program to build demand for this summer season and beyond.

"However, as we've always said, if more needs to be done, we will do it, and we will continue to engage closely with the King Island community in the weeks and months ahead."

Public Health was asked if it stood by the decision to make the travel warning.

It did not provide a response.