"In terms of our borders currently, anyone who comes from a high-risk country is placed into self-isolation or quarantined for a period of two weeks," he said on Sunday.

"We do have I think the unique circumstance where we are an island within an island so I think it's appropriate that we take stronger measures than perhaps other states might take and we're looking at those.

Full coverage: Click here to see the latest on coronavirus in Northern Tasmania

"I won't be shutting our border but what I will be doing is ensuring we manage it to provide a more robust protection to Tasmanians."

Labor leader Rebecca White on Sunday said consideration should be given to greater screening of passengers at airports and on the Spirit of Tasmania vessels

She said passengers should have their temperatures taken and their details recorded at least.

Greens health spokeswoman Rosalie Woodruff said the government needed to impose stricter controls over visitors to Tasmania and require all those who arrived to the state by air or sea to self-isolated for 14 days.

She said the government needed to advise Tasmanians to avoid all non-essential travel interstate or overseas.

Australian Medical Association state representative Helen McCardle on Friday said school closures should be more seriously considered.

Mr Gutwein said he had received no advice yet on school closures or on an extension of the Easter holiday period for schools.

Mr Gutwein said he did not believe parents who removed their children from schools due to fear of coronavirus contraction would be penalised as it was in the interests of a child's health and wellbeing.