Five more people in Tasmania were diagnosed with coronavirus on Saturday, taking the state's total to 16 confirmed cases.
A woman and two men who travelled on the Ruby Princess cruise ship and another woman and man who travelled together in Europe.
Tasmania's Director of Public Health Mark Veitch said the cases brought the total number diagnosed in the state to 16.
Coronavirus: All the latest updates on COVID-19 for Tasmania
The total figure does not include the additional Tasmanian woman, who was also on the Ruby Princess cruise ship, who was diagnosed with COVID-19 in Sydney.
"Contact tracing of all these recent cases is underway," he said.
"Persons who are identified as close contacts will be required to remain in quarantine for 14 days after contact with the case.
"This will include persons who were seated near cases on flights when cases may have been infectious."
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Dr Veitch said because of the emerging evidence of virus infection among Ruby Princess passengers, both NSW Health and the Tasmanian Department of Health had contacted the 54 Tasmanian residents who were on the cruise.
"Assessment and testing for coronavirus is being arranged for those with symptoms," he said.
"All passengers will be required to remain in quarantine for 14 days after return to Tasmania."