After three days with zero new coronavirus cases, Premier Peter Gutwein used his coronavirus address on Monday to affirm that Tasmania would "continue to march to the beat of its own drum."

"We have an older and more vulnerable population, that has been front and centre and driven our responses from the start," he said.

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"Even though we have had three days with zero cases, it is not over yet."

Mr Gutwein thanked the people in the North-West regarding their adherence to the extra restrictions put in place as a result of the outbreak at the North West Regional Hospital and the North-West Private Hospital.

Tasmania has 44 active cases of coronavirus across the three regions, however, as testing capacity increases, Mr Gutwein said it was inevitable that more cases would be found.

"This week will be an important week for Tasmania," he said.

"It will be the week where we outline how we go back to some level of normality."

However, he said social distancing measures would be in place until a vaccine was found, that was vitally important.

"On the weekend I went North and it appeared there were more traffic on the road. Anecdotally we are hearing people are moving around more," he said.

"I can understand why people are doing this, we are in a good place, but we need to be sensible and responsible. Don't let the virus travel with you."

Mr Gutwein said National Cabinet will meet on Monday to be briefed on the road map to lifting restrictions and that it will meet again on Friday to finalise the response.

Tasmania's response to lifting restrictions will be a staged response and the timeframes around that response will be outlined on Friday.

Mr Gutwein said he would be able to provide more detail along with times for the staged response Tasmania will use to lift restrictions.

"We will be putting time frames around those so Tasmania understand absolutely what the steps will be," he said.

Dr Scott McKeown reiterated that Tasmania had not had a stable level of the number of cases and the North-West outbreak was under control but not over.

He said it was important that people listened to the advice coming from the state and that advice was restrictions, social distancing and hygiene, were followed.