Mr Gutwein returned to the North of the state over the weekend to be with his family after a number of gruelling weeks at the helm of a state in the grips of a public health crisis.

He said he and his family drove to the city yesterday to purchase essential supplies - and what he saw as he looked out the car window disturbed him.

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"I was very concerned about the number of people that were still out and about, browsing shops, moving throughout the community," the Premier told reporters this morning.

"Many, I'm sure, were doing what we were doing, and that is out purchasing essential food and supplies; but many, it appeared, were not.

"There were some children in groups in the mall and walking through the city."

Mr Gutwein acknowledged the challenges for the community when it came to the state government's measures to limit the spread of COVID-19.

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"I know this is tough, I know this is hard," he said. "And I've had many discussions over the last 24 hours with my own family and children about the need for [the restrictions] to occur."

"While I'm sure the majority of Tasmanians are doing the right thing, we know it will take everyone to do the right thing to ensure that we can flatten the curve and keep our state safe."

The Premier reiterated that people had to stay at home unless they needed to:

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