Mr Gutwein on Tuesday indicated some of the island's coronavirus restrictions could be eased ahead of schedule before the June long weekend.

He revealed he had spoken to some state and territory leaders about borders but reiterated he would wait until at least July before making any decision on when and if Tasmania would reopen.

"We'll be guided by public health. I would just encourage all of the premiers around the country to stop what appears to be this game of one-upmanship," he said.

"I won't comment on the way the Queensland premier deals with her borders nor how the NSW premier deals with hers.

"It's quite obvious the federal government has a view but my job is protect the best interests of Tasmanians."

Tasmania is due to progress to stage two of eased restrictions on June 15, having opened cafes and restaurants for up to 10 people last week as part of stage one.

Mr Gutwein said there could be some earlier easing before the June 8 Queen's birthday long weekend.

He reiterated any decision would be based on health advice and high levels of testing.

About 300-400 people are being tested each day but the state's public health service wants the figure to be closer to 700.

Tasmania has gone 11 days without recording a new coronavirus case after none emerged on Tuesday. Just seven cases have been confirmed this month.

The state's number of active cases has dropped to eight while 205 people from a total 226 confirmed cases have now recovered.

"If this was a football match, we're now in the last quarter. The wind is at our back, but it ain't over 'til it's over," Mr Gutwein said.

Australian Associated Press