Tasmania has five new confirmed cases of coronavirus, taking the state's tally to 47.

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.

Authorities said two of the cases were children, two were adults in their 30s and one was aged in their 70s.

Three of the cases are from Northern Tasmania, two are from the north-west.

All of the cases were passengers aboard the Ovation of the Seas, which docked in Sydney on 18 March.

The Department of Public Health said there remained "no evidence of community transmission in Tasmania, as all the cases are directly or indirectly linked to overseas travel".

All of the cases were already in self-quarantine and receiving daily contact from department staff as they were passengers on a cruise ship where coronavirus cases had been detected.

The two children had not been attending school.

Second relief package welcomed

The Tasmanian Government announced on Thursday it would refund public school levies, freeze water prices and cap electricity prices as part of a second coronavirus stimulus package announced today.

The second tranche of support brings the State Government's coronavirus contribution to almost $1 billion, an unprecedented amount announced by a tearful Premier Peter Gutwein as he expressed regret at widespread job losses triggered by the COVID-19 pandemic.

Aurora Energy will not disconnect any residential or commercial customers during the crisis.

A series of no-interest loan programs for small-to-medium businesses and the local government sector have been extended.

The electricity bills of small businesses will be waived for the quarter from April.

Whether and how the State Government will deal with making up any lost revenue from these measures is unclear.

The state budget has been delayed until October when these kinds of issues will be dealt with.

The Premier has indicated bigger price hikes later will be avoided as far as possible.

"We had strong balance sheet going into this and I intend to use it," Mr Gutwein said.

Tourism body praise for 'life raft'

The school fee waiver is expected to cost the State Government $13 million, and the cap on electricity prices and freezing of water prices about $20 million.

The local government no-interest loan scheme is expanding from $50 million to $150 million, and the range of electricity relief measures will result in a shortfall of about $41 million.

The measures were described as a "life raft" for the sector by Tourism Industry Council Tasmania chief executive Luke Martin.

"Our sectors have been doing the heavy lifting for the Tasmanian economy for years," he said.

"It is reassuring to see that in our hour of greatest need, the State Government has responded accordingly," he said.

The Tasmanian Council of Social Service acting chief executive Simone Zell commended Mr Gutwein on his "strong leadership".

"More than 120,000 Tasmanians were already struggling to make ends meet before this crisis began," he said. "Now, thousands more Tasmanians are out of work and relying on community services to simply get by."

"Our message is simple, we are here for you."

In other developments late on Thursday, the State Government announced it would be closing all national parks and reserves at midnight, extending a ban already imposed on some of the more popular destinations and campgrounds.

That means no day or overnight walks, fishing, mountain biking or other outdoor activity will be allowed in any park or reserves in Tasmania.

This extends to all facilities and on-site public services.

Refunds for cancellations

Earlier, the Premier told travellers not to come to the state and anyone already here to "go home", as he flagged that a "hard lockdown" could last as long at six months.

Mr Gutwein used his daily press conference on Thursday to urge travellers to stay away.

Tourists must undergo 14 days of quarantine after arriving in Tasmania. ( Supplied: Natalie Mendham )

"We're built on tourism, so it hurts me to say that but do not come and put Tasmanians at risk," he said.

"We're an island and we are unique in that regard. We have used our island state as an advantage."

Mr Gutwein said he had directed TT-Line, the operators of the Spirit of Tasmania, to "prioritise its bookings to ensure that only Tasmanians returning, freight and those travellers who have met essential traveller or exemption criteria, are able to travel".

"Any non-essential travellers, including Tasmanians, who do return will be subject to the 14 day self-isolation period as is currently the case.

"Full refunds are being provided for all cancellations and no amendment fees are being charged," he said, adding the current imperative for caravan park visitors to vacate this Sunday has been extended until April 1.

Last week, the State Government announced strict border measures requiring all "non-essential" travellers into the state to go into 14 days' quarantine.

Mr Gutwein said the state would go into a "hard lockdown" if he received advice that it should.

"A hard lockdown isn't two weeks, it's not four weeks. A hard lockdown could be six months," he said.

"This is a very difficult time but as a state we have to take every step that we can to ensure the health, wellbeing and safety of Tasmanians," he said.

No evidence of community transmission

Health Minister Sarah Courtney said six people were diagnosed with coronavirus on Thursday - four women and two men.

"There remains no evidence of community transmission in Tasmania," she said.

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Authorities said three of the six new cases were in northern Tasmania, two were in southern Tasmania and one case was in the north west.

The Tasmanian Health Service (THS) said two of the cases were aged in their 70s, one was aged in their 60s, one in their 50s, one in their 30s, and one in their 20s.

The THS said two of the cases had recently been on cruise ships, one case was a close contact of a previously confirmed case, and three had recently travelled to Tasmania from overseas.

Director of public health Dr Mark Veitch said they were in contact with a number of Tasmanians who had been on board cruise ships.

"We have 240 people on cruise ships in self-isolation and being actively monitored," he said.

"There's another 80 people who are close contacts of cases who we also have under active monitoring and self-isolation."

Dr Veitch said Tasmania's testing guidelines had been in line with the national ones all along.

"There's been an expansion of testing criteria, which includes all people from the mainland who have symptoms," he said.