The small minority of Tasmanians not doing the right thing are putting lives at risk from coronavirus, Premier Peter Gutwein says.
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"I think in the main Tasmanians are doing a pretty good job, but there is no room for complacency," Mr Gutwein said on Wednesday as the battle against the killer pandemic continued.
"At the end of the day, it's not the 95 per cent of people who follow the rules, it's the 5 per cent that don't.
"They will be the ones that will cause Tasmania problems."
He said they would cause problems for their families, for communities and for the state.
There have been gripes about some of the measures taken by the state government and government agencies and businesses aimed at limiting human interaction to slow the spread of the virus, with some people arguing things which were banned were less unsafe than permitted activities, such as visiting supermarkets.
Mr Gutwein stood by all of the measures.
"We are dealing with people's lives here and I think it's important that people recognise that," he said.
Restricting travel to and from the North-West or Burnie was being discussed, partly due to an outbreak at the North-West Regional Hospital in the city.
"At this stage, I haven't been advised (by medical experts) to do that," Mr Gutwein said.
"What North-West residents need to do is stick to the rules.
"The simplest way we can get on top of this is to ensure North-West Coasters are self-isolating when they are asked to, good social distancing practices and following the rules."
Mr Gutwein said the three Tasmanian coronavirus deaths by Wednesday morning saddened him.
"I want deaths to be as low as possible," he said.
"If we self-isolate, social distance and follow rules we lay down, we will keep deaths to an absolute minimum."
Braddon Labor MHAs Anita Dow and Shane Broad urged North-West residents to stay vigilant and follow the rules to protect themselves, those they loved and their communities during the region's COVID-19 outbreak.
"This outbreak in our community is of great concern and we must do all we can to contain it," Ms Dow said.
"We support Peter Gutwein's call for North-West community leaders to help spread the message and ensure people stay home wherever possible.
"This means only going out for essential services and supplies and following social distancing guidelines at all times."