It comes after the Queensland government was forced to apologise to the family of Nathan Turner.

The 30-year-old tested positive for the virus after he died in the small town of Blackwater last week.

However, on Monday a coroner advised subsequent tests had returned negative results.

Tasmania's director of Public Health Dr Mark Veitch said false results were rare, and that the state's tests were being conducted by experienced microbiologists.

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"You may recall some weeks ago that I described an equivocal cases, where a case gave a partially ... positive result," he said.

"They were subsequently retested and we believe it actually represented a kind of false positive. We come to those conclusions by discussing the test results with the microbiologists. Particularly, if you are not expecting a result to be positive, you need to ask more critically the question - could that have been a false positive?"

Dr Veitch said there had only been three cases of COVID-19 in Tasmania that didn't have a coherent link to a likely source of infection.

"I am confident that we were making the right call in our diagnosis here," he said.

Health Minister Sarah Courtney has urged Tasmanians to remain vigilant as stage two restrictions are brought forward, with an average of 400 COVID-19 tests being conducted a day.

"This is one of the critical pillars that we have going forward to ensure we can move on to stage 3 in a carefully considered way."

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