Four new cases of coronavirus have been confirmed in Tasmania, taking the state's tally to 86.

The increase in cases came after Burnie's hospital shut two wards to new admissions after three staff members were infected with coronavirus, prompting an investigation into the incident.

Tasmania COVID-19 snapshot Confirmed cases: 226

Confirmed cases: 226 Deaths: 13, 12 in north-west What do I do if I think I have coronavirus? If you think you might have COVID-19 phone your GP or the Tasmanian Public Health Hotline on 1800 671 738. Need an interpreter? Phone the Translating and Interpreting Service on 131 450 and tell them your language. For more information and factsheets: Visit the Tasmanian Government's coronavirus page here.

Three of the new cases revealed on Sunday night are female and one is male.

Two are from northern Tasmania and two are from the north-west.

One is aged in their 40s, one is in their 60s and two are in their 70s.

Of the two cases in northern Tasmania, one is associated with the Ruby Princess cruise ship and the other was in contact with another case, but no other information has been released about the cases from the north-west.

In other developments on Sunday, Tasmanian Premier Peter Gutwein forewarned of even tighter restrictions after witnessing firsthand members of the public flouting social-distancing rules, with police today advising they had arrested a man for "non-compliance with COVID-19 isolation requirements" following a tip-off from the public.

Three health workers at the North West Regional Hospital, in Burnie, hospital have now tested positive for the virus. The latest person is aged in their 20s.

At the Sunday morning public briefing, director of Public Health Mark Veitch said an outbreak investigation involving the hospital and government agencies was now underway.

"This is obviously a much more complex investigation than usual and it will involve investigation into the community to discover whether there is any source of infection for these people," he said.

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Chief Medical Officer Tony Lawler said the surgical and medical ward at the hospital would stop patient admissions as a result of the infections.

Tony Lawler said surgical and medical ward admissions at the hospital were on hold. ( ABC News: Tony King )

"We're not talking about transferring patients who are on those surgical and medical wards to other hospitals, we're talking about patients who are presenting to the emergency department and who are not suspected of having COVID-19," he said.

Professor Lawler said anyone needing admission may be transferred to the Mersey Hospital in Devonport, the Launceston General Hospital or the co-located private hospital.

Dr Veitch said about 18 staff were now in isolation after being in contact with the infected staff members.

A school-aged child identified as the second positive case yesterday had been travelling with a family member on the Ovation of the Seas cruise ship and had been in quarantine after arriving back in the state, Dr Veitch said, adding the child had not attended school since returning.

The child was "well enough to be managed at home," Dr Veitch said.

Three cases involving staff who tested positive to coronavirus are now being investigated. ( ABC News )

More than 3,000 COVID-19 tests had been conducted in the state as of yesterday, with a total of 82 people returning positive results since testing began.

Dr Veitch said 26 of those infected had been since discharged from care.

He rejected calls for frontline health workers and police to undergo testing.

"If you test people who are well and get a negative test, it doesn't mean they won't get sick the next day," he said.

"And it can provide a false sense of reassurance to people."

Push for more PPE and wider testing for the frontline

The CEO of Rural Health Tasmania, Robert Waterman, said accessing personal protective equipment (PPE) for health workers was still a challenge.

"We're doing the best that we can to get our hands on as much of it as we can but it's been difficult," he said.

On Saturday, Health Minister Sarah Courtney said more masks, hand sanitiser and gowns were on their way to Tasmania.

Mr Waterman also called for more community testing.

"You're never going to get an understanding of community transmission unless you test people in the community," he said.

Opposition Leader Rebecca White said emergency service workers on the front line should have access to priority testing.

"It is about making sure that if any of those emergency service workers display symptoms they can access testing immediately," she said.

"That will either help us to track and trace if they do test positive, or if they're negative it will mean that they're able to go back into the workforce very quickly."

Man arrested for 'refusing to abide by isolation requirements'

On Sunday, Tasmania Police said they had "responded to reports of a man refusing to abide by isolation requirements after his recent return to Tasmania from Victoria".

The 50-year-old man had been "provided accommodation at a government facility for his period of isolation", police said.

"As a result of investigations … it was established that a number of breaches of the isolation requirement had been committed by the man.

"As such, police arrested the man at the facility and returned him to Launceston Police Station."

The man was charged with offences under the Public Health Act 1997 and granted bail with conditions to appear in the Launceston Magistrates Court at a later date.

The man was then returned to the government facility to continue his period of isolation, police said.

News of the man's arrest comes as Mr Gutwein foreshadowed a further toughening of measures to stop the spread of the virus, saying he had witnessed firsthand members of the public seemingly ignoring social-distancing advice.

Mr Gutwein said he "sat in the car with the children, while my wife went in" to do the shopping in Launceston.

"I was very concerned at the number of people who were out and about browsing shops, moving throughout the community … many appeared to be buying essential supplies, many were not," he said.

He said he had also heard reports of "long lines of people" outside of Hobart's farmers' market with "no social distancing occurring".

"I think today is the last day of the farmers' market," he said.

"It's not a game. We've got a long way to go.

"We have gotten in early, we have put these restrictions in place and we have a chance to flatten the curve and ensure that we don't become an Italy, or a Spain, or New South Wales or a Victoria."

"We are in front, but we've got to make certain that we stay there."

Late on Sunday Mr Gutwein said that after being contacted by Hobart Lord Mayor Anna Reynolds he would reconsider closing the Hobart farmers' market.

But he said responsibility for ensuring social distancing and appropriate hygiene practices at the market would rest with the council.

Mr Gutwein said boat owners should only use boat ramps near where they lived.

"If you own a boat, you will be restricted to launching that boat within the municipality in which your primary residence address is listed," he said.

He said the move was designed to ensure people did not congregate at boat ramps over the Easter break.

Attorney-General Elise Archer announced that due to the ongoing pandemic, the Legislative Council elections for the seats of Huon and Rosevears — which were due to occur next month — had been deferred.

She said it was anticipated the elections would be held before the end of August, when the Legislative Council would next sit.

Deferral 'impacts on Tasmania's democracy', Greens say

Tasmanian Greens Leader Cassy O'Connor issued a statement, describing the deferral as a "matter of real concern … that the decision, which impacts on Tasmania's democracy, was not dealt with by Parliament".

"Tasmanians are likely to be living this reality for the foreseeable future. Our democratic institutions need to be robust enough to adapt and function," she said.

"In the absence of Parliament playing a role in the decision to defer the Huon and Rosevears elections, there has to be real clarity and openness about the process of what will happen from here, particularly given the likelihood physical distancing will still be a necessity on August 25."

Ms O'Connor said the Greens welcomed "the Premier's stated commitment to be open and transparent about decisions being made under the emergency powers Parliament gave his Government on trust and those already considerable, necessary powers vested in the director of Public Health".

"There's growing community concern to see parliamentary oversight continue in this time of emergency," she said.

"Given the uncertainty over whether there'll be any real change to physical distancing advice by August, the Tasmanian Parliament needs to find ways to meet electronically as a priority."