There are now 22 people in Tasmania who have tested positive for coronavirus, with five people being diagnosed today, the director of Public Health says.

Key points: Tasmanians told they need to "do better" in observing the measures to stop the spread of coronavirus

Tasmanians told they need to "do better" in observing the measures to stop the spread of coronavirus The tally of people testing positive reaches 17 — all are people who became infected before arriving in the state

The tally of people testing positive reaches 17 — all are people who became infected before arriving in the state Sunday's National Cabinet meeting may result in further tightening of Tasmanian policy

This brings the number of confirmed cases to 15 in the state's south, two in the north, two in the north-west and three who lived interstate.

The five confirmed cases today all returned to Tasmania from overseas — two from the United States, two from the Ruby Princess cruise and one from the Ovation of the Seas cruise.

Public Health director Dr Mark Veitch said the cases "reflect the rapidly increasing incidence of coronavirus infection throughout the world", and the occurrence of cases on cruise ships.

"Public Health Services is speaking daily with passengers from the Ruby Princess cruise who are all required to be in quarantine until April 2," Dr Veitch said.

Meanwhile, the Tasmanian public has been warned they would face the "full brunt of the law" if they fail to observe the self-isolation protocols in place to mitigate the spread of coronavirus.

At a press conference on Sunday, Premier Peter Gutwein said people who were directed to enter self-isolation after being diagnosed as positive for the COVID-19 illness "must do that".

"It is important that people follow the rules. If you have been asked to self-isolate, to quarantine, then you must do that … you cannot go to the shop, you cannot have friends around, you cannot go to a place of worship," he said.

"We are doing a good job, but we need to do a better job. This is serious."

Mr Gutwein said people who were instructed to go into quarantine "must stay in self-isolation", adding that people who "flout the rules" would face the "full brunt of the law against you".

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The ABC has reported Victoria and New South Wales are moving to stop non-essential activities in the next 48 hours, which include the closure of non-essential businesses such as restaurants and pubs.

Victoria will also move its school holidays forward to Tuesday.

Asked if he was still sending his own children to school in Tasmania, Premier Gutwein said "yes, I am".

Second stimulus package on its way

Mr Gutwein said the possible closure of schools was also on the agenda for discussion at tonight's National Cabinet meeting between the Prime Minister, premiers and chief ministers.

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The State Government said it was working on releasing a second stimulus package "that will help Tasmanians even further".

Mr Gutwein said it would be announced in the "coming days".

"The coming months will be hard on Tasmanians as we deal with the ongoing impacts the coronavirus pandemic is having, but the most important things we can do are stay calm and follow the advice from health professionals," he said.