Tasmania will toughen restrictions to stop people heading to their holiday homes or taking boating trips over the Easter break.
Premier Peter Gutwein said many elderly people lived in these areas, and they needed to be protected, as the state's confirmed cases rose to 82.
"We must not see during these holidays a flurry of people into those vulnerable communities," he told reporters on Sunday.
"If you are on a boat, you will be restricted to launching that boat within the municipality within which your primary residential address is listed for the purposes of the stay-at-home restrictions."
He said it was tough, but necessary.
"I want to ask you to work with me on this, but importantly, the rules are the rules, and if you break them then the full force of the law will be brought down on you."
Legislative Council elections for the divisions of Huon and Rosevears, due to be held in May, have also been delayed till at least August.
Staff and patients at a hospital in Tasmania's north west may need to be tested for coronavirus after a third worker at the facility was confirmed as having COVID-19.
The woman in her 20s, who works at North West Regional Hospital in Burnie, was one of two fresh cases of COVID-19 in Tasmania confirmed on Saturday evening.
The other was an eight-year-old girl from Tasmania's north.
Two staff members at North West Regional Hospital had already been confirmed as having the virus on Friday.
Tasmanian Chief Medical Officer Professor Tony Lawler said an investigation had begun to identify and contact anyone who has had close interactions with the woman in her 20s.
Any patients or other staff believed to be at risk of COVID-19 will be assessed and tested.
"If 'Fortress Tasmania' is going to work, if our strong border controls that we put in earlier than other states, if the fact that we banned cruise ships earlier than other states are going to work for us, and if we are going to get through this and flatten the curve, we need to follow the rules," Mr Gutwein said.
Australian Associated Press