Tasmania has recorded its second coronavirus death, with both cases linked to the Ruby Princess cruise ship.
A man in his 80s died at the Royal Hobart Hospital overnight, taking the national COVID-19 toll to 19, Premier Peter Gutwein said on Tuesday.
It comes after a woman, also in her 80s, died in the state's northwest on Monday.
"This is a very sad time. It serves as a warning to us all that these are going to be tough and difficult times," Mr Gutwein said.
The elderly man had been a passenger on the ship, Public Health Director Mark Veitch confirmed, but the woman's connection is unclear.
The Ruby Princess has been a major source of virus spread in Australia since infected passengers were allowed to disembark in Sydney without adequate checks two weeks ago and then return home interstate.
At least five people connected to the ship have died from coronavirus, while a total of 211 passengers have been infected.
Tasmania, meanwhile, has 69 cases of the virus. Ten of those people have recovered.
Authorities have stepped up efforts to find the source of two cases, a healthcare worker and woman in her 20s, at Devonport in the state's northwest.
Dr Veitch hasn't ruled out community transmission and hoped more details would be known in coming days.
"Both of them had contact with people from overseas and interstate within Tasmania," he said.
"It's always possible infection was acquired from one of these sources rather than within the community."
Tasmania has yet to record evidence of community transmission.
The Royal Hobart Hospital has tightened visitor restrictions from Tuesday to a daily four hour window from 2pm to 6pm.
Only one visitor is permitted per patient for a maximum of 30 minutes.
For at least four weeks, people have been ordered to stay home unless they are getting essential supplies, going to work or school, exercising, attending a medical appointment or providing care.
Those who disobey could be arrested, charged and fined up $16,800.
"Social distancing and abiding by the rules will save your life, it will save your family's lives, it will save lives in our community," Mr Gutwein said.
About 90 rooms at state-government-controlled hotels are being used for people in quarantine.
Australian Associated Press
