Premier Peter Gutwein said New South Wales had been considered a medium-risk area and arrivals from the state have had to either quarantine in their primary residence in Tasmania or at a government hotel.

He said Public Health had given further consideration to the state's dealing with coronavirus and decided to classify it has a low-risk area from next week.

The state's borders were lowered to South Australia, Queensland, Western Australia, Northern Territory and the ACT on Monday.

Mr Gutwein said systems around arrivals to the state had performed to plan.

He said nobody who came to the state on Monday was referred to take a coronavirus test after having their health screened.

Mr Gutwein said he was heartened through media coverage to see people reunited.

"The fact there were so many families able to reunite yesterday was a result of Tasmanians doing the right thing," he said.

"But it's important we don't rest on our laurels."

Mr Gutwein said the decision to open to New South Wales could change if there was another outbreak in the state.

"They look on balance very safe in terms of their population size and the relative risk to Tasmania," he said.

"But obviously, we will take public health advice along the way."

Public Health director Mark Veitch said an area with less than five cases from an unknown source over a 28-day period would classify it as a low-risk area.

There have been six of these cases in New South Wales over the past 28 days.

It is anticipated the state will open to Victoria on December 1, though this will rely on Public Health advice.

It has been two days since a new coronavirus case was diagnosed in that state.

Tasmania has gone 76 days without a new case.

Dr Veitch again pleaded with the public to continue to get tested for the virus, noting testing levels remained below the benchmark.

There were 320 tests taken on Monday.

Dr Veitch said there should be at least 550 tests taken a day.

He said Launceston in particular had quite low testing levels.

"So I would certainly be encouraging people in the North of the state to get tested," Dr Veitch said.

A number of internal restrictions continue to be in place in Tasmania, such as caps on gatherings and requirements for people to sit down in pubs.

Dr Veitch said these restrictions would considered over the next three weeks.

He said if new cases emerged within states Tasmania had opened to, travel restrictions would be reconsidered.

"We will over the next several weeks consider the safety of any further relaxation of measures," Dr Veitch said.

He said this would be encouraged by better gathering of patron information at hospitality venues.

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