Testing for coronavirus has stepped up at Devonport in northern Tasmania, where two hospital staff are among the latest cases.
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The island state had recorded 80 COVID-19 cases as of Friday night after six new positive tests, but there is yet to be evidence of community transmission.
Two staff members of the North West Regional Hospital are among the latest cases to test positive to coronavirus, the state's chief medical officer Tony Lawler confirmed in a statement.
An investigation is underway to identify and contact anyone who had close contact with either of these staff, inside and outside the hospital.
The Tasmanian Health Service has established an incident management team, to ascertain who may be at risk of exposure at the hospital.
It comes as testing criteria in the town has been widened, with anyone showing virus symptoms now able to be tested, Deputy Public Health Director Scott McKeown said.
He said further information on the likelihood of community transmission would be provided next week once a sufficient number of tests had been taken.
Two elderly people died from the virus in Tasmania earlier this week but the rate of new COVID-19 cases has slowed.
Premier Peter Gutwein said the state's daily average increase in cases was behind the national figure - about five per cent compared with seven per cent.
However, he said tough social restrictions will not be eased.
Mr Gutwein warned the virus fight was nowhere near over, and flagged tough policing of the two-person gathering restrictions could be extended beyond the initial four-week timeline.
"We need to be disciplined, we need to be responsible and we need to focus on ensuring that we follow the rules," he said.
Police will attend weekend farmers' markets to make sure people are obeying social distancing rules.
Meanwhile, it was announced state schools will open a day later for term two, on Tuesday April 28.
Students will be able to attend school if they need to, but the state government has reiterated children should be kept home where possible and learn online.
School attendance rates have plunged to about nine per cent from the usual high in the 80s.
Australian Associated Press
