Tasmania has recorded its first death from coronavirus, as the state is warned breaking new rules on public gatherings could result in arrest.

Key points: From midnight, Tasmanian Police can arrest people in public groups larger than two, if they are "breaking the rules"

From midnight, Tasmanian Police can arrest people in public groups larger than two, if they are "breaking the rules" The tightening of measures come after a woman in her 80s died while being treated for COVID-19

The tightening of measures come after a woman in her 80s died while being treated for COVID-19 The Premier said Tasmanians needed to take the situation seriously and that people's lives were at risk

Premier Peter Gutwein confirmed a woman in her 80s died in the North West Regional Hospital in Burnie this morning.

Speaking at his daily press conference, the Premier said Tasmanians should not underestimate the gravity of the situation.

"I have been saying for weeks that this is serious, that people will die and unfortunately Tasmania now has its first death," he said.

"All Tasmanians need to accept and understand that this is not a game, this is serious, people's lives are at risk."

Late on Monday, authorities confirmed three new cases, taking the state's total to 69.

Two are from southern Tasmania and one is from the north-west.

One is a close contact of a known case, one is a recently-arrived traveller from overseas, and the third has recently travelled aboard a cruise ship.

All three cases are women.

Public Health Services is continuing to investigate two cases in the Devonport area to determine a likely source of infection.

The Premier also confirmed the Tasmanian Government would enforce the new ban on social gatherings, reduced from 10 to two people, from midnight tonight — warning people would face "arrest" if they did not comply.

Mr Gutwein said while most people had observed the measures, "there are some who haven't".

The Premier says people will be committing an offence unless they are leaving home for essential purposes. ( ABC News: Billy Draper )

"So, from midnight tonight, unless you are going to work or school, getting essential or medical supplies, exercising [or] providing compassionate care, you will need to remain in your primary place of residence and you will be committing an offence if you don't," he said.

"If you want to go for a walk, you can do it with one other person. A bike ride, play golf, run, a horse ride, it can only be with one other person."

"Our police will ensure that they enforce this — you'll be able to be arrested, you'll be charged and summonsed."

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The order follows the announcement of a national ban on gatherings, by Prime Minister Scott Morrison and will be in place for four weeks and reviewed after that, Mr Gutwein said.

Mr Gutwein said he had "the department at the moment looking at a range of on-the-spot fines" of between $750 to $1,000.

"These are tough measures, but they're done with Tasmania's health, wellbeing and safety as our first priority."

People with holiday homes will not be allowed to travel between their primary and secondary residences.

Director of Public Health, Dr Mark Veitch, said the deceased woman "had been unwell for several days" and "any family members who need to be in quarantine are in quarantine".

The national COVID-19 death toll is 17.