Concerns on social media a large number of mainlanders are entering Tasmania in caravans are unfounded says Premier Peter Gutwein.
"I have been informed that the only campervans that have been carried on the last two sailings [of the TT-Line], the sailings this week, are caravans that have been owned by Tasmanians," Mr Gutwein said.
As of Thursday, TT-Line is prioritising returning Tasmanians, freight and essential travellers and extra sailings have been added.
Coronavirus: All the latest updates on COVID-19 for Tasmania
"We will let Tasmanians come home. We will not turn our back on our people," Mr Gutwein said.
"Many Tasmanians are either travelling on the mainland or, in many cases, Tasmanians house their vans on the mainland. It's cheaper. But they are bringing them home.
"In terms of vehicles that may be travelling on the Spirits that have mainland plates, there are many Tasmanians, students and others, who live on the mainland [and] they are coming home."
Mr Gutwein said there was more campervan or caravan travel in the state because people were moving north to the ferry terminal, with the imminent closure of accommodation to non-essential persons and non-residents pushing visitors to leave Tasmania.
"We're getting them out," Mr Gutwein said.
Mr Gutwein said border controls on Tasmania's mainland also applied to the state's islands meaning non-essential travellers entering King and Flinders Islands have to self-isolate for 14 days after entering.
He said he did not want Tasmanians travelling to the islands for a holiday.
Mr Gutwein noted good weather was expected this weekend and urged Tasmanians not to go out and congregate.
"Don't go barbecue with your mates or booze up in the park. You need to be sensible," he said.
"Stay home if you are not at work or school or out buying essential supplies. Stay home and save lives."
He also said shack owners should stay home over the Easter period and not converge on small communities.
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Mr Gutwein said schools would remain open but as of Monday parents who could keep their children at home and supervise them should.
"Where possible, from Monday, parents should keep their children home from school," Mr Gutwein said.
Mr Gutwein said a national cabinet meeting would be held on Friday to discuss further social distancing measures.
"Lockdown measures are being spoken about [by Victoria and New South Wales]," he said.
"If we need to do it, we will do it.
"These are unprecedented times and I will keep making the decisions that are needed to get our state through this."
But Labor leader Rebecca White said the inability to monitor people coming into Tasmania on the Spirits highlighted the need for a broader lockdown.
"A broader lockdown would send a strong and consistent message for people not to come to Tasmania at this time," Ms White said.
"Tasmania still has an opportunity to contain the spread of the virus, but only if we act quickly and decisively."
There are now 47 confirmed cases of coronavirus in Tasmania with five cases diagnosed in the past 24 hours.
Health Minister Sarah Courtney said she wanted to assure Tasmanians two of the new cases who were children did not attend school.
Public Health director Mark Veitch said all five of the new cases were passengers on the Ovation of the Seas cruise ship and were in quarantine after returning to the state.
"We have five cases who have cleared their infection, we have five cases being managed in hospital and the remaining cases are being managed in home or home-like circumstances," Dr Veitch said.
Dr Veitch said Public Health was monitoring the isolation of 268 people who were off various cruise ships and 36 people who were household contacts of previous cases.
He said 400 spot checks have been conducted on people in quarantine.