The continuation of the lockdown in the South of the state after Monday's 6pm cut-off will depend on the COVID-19 test results received Sunday and Monday.
As of Saturday morning, Premier Peter Gutwein said 158 primary close contacts had been discovered, which included contacts from the Bridgewater Woolworths exposure site.
Public Health director Dr Mark Veitch said there had been a big jump in the number of primary contacts compared to Friday's numbers.
However, there were no new cases from the 40 test results that had been returned and no new exposure sites were declared.
The snap three-day lockdown in the South came after the escape of a COVID-positive traveller from quarantine in Hobart earlier this week.
"I am very pleased to say this morning we have no further positive cases at this time," Mr Gutwein said on Saturday.
Those not residing in the 12 municipalities affected by the lockdown have been told not to travel to the areas.
"It's important the steps we are going through at the moment. We have acted swiftly. We have acted decisively with a view that this does not get away from us," Mr Gutwein said.
Mr Gutwein said in Saturday's update that during the previous 24 hours there had been 1402 COVID-19 tests.
Of those tests, 576 were carried out at the Gagebrook testing site and 648 were from Macquarie Point.
"Our aim is not to prolong [the lockdown] ... short and sharp as possible," Mr Gutwein said.
"It's taken one individual to do the wrong thing and leave the heavy lifting to everyone else."
Nineteen casual contacts related to the positive COVID-19 case were identified previously, but no others were added on Saturday.
Dr Veitch said more testing and working through referrals would be undertaken over the next few days, with the results to determine whether the lockdown would be extended or not.
Mr Gutwein reiterated there was financial support available for those affected by the lockdown.
Meanwhile, Labor saw the lockdown as an opportunity to bring Tasmania's homelessness and housing crisis to the forefront.
Labor spokesperson Ella Haddad said hundreds of Tasmanians needed urgent assistance while there was a risk of COVID-19.
"The stark and simple fact is that Tasmanians can't comply easily with lockdown instructions without a home," she said.
"The government needs to be prioritising the well-being of the most vulnerable people in our state and providing shelter.
As of Saturday, Tasmanians had achieved an 83 per cent vaccination rate for first dose, with 68 per cent fully vaccinated.
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State health commander Katherine Morgan-Wicks issued a plea to people residing outside of the lockdown to get vaccinated.
"People outside the lockdown area, specifically in Northern and North-West Tasmania, [can look at what is] happening in Southern Tasmania and make sure they are doing everything they can to get themselves, along with their family and friends, vaccinated," she said.
"Vaccination appointments are available from Smithton to Scottsdale, including a mobile clinic at St Leonards on Monday and Westbury on Tuesday, so please call the Public Health Hotline on 1800 671 738 to make a booking."
Mr Gutwein said the next 48 hours remained critical and asked Tasmanians to work together to get on top of the situation.
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