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Second coronavirus death in Tasmania

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Tasmania has recorded its second coronavirus death, with an elderly man dying at the Royal Hobart Hospital overnight.

It comes after a woman in her 80s died on Monday from the virus in the state's northwest and takes the national COVID-19 toll to 19.

"This is a very sad time. It serves as a warning to us all that these are going to be tough and difficult times," Premier Peter Gutwein told reporters on Tuesday.

The man was aged in his 80s.

Both deaths are associated with travel on the Ruby Princess cruise ship, the state government confirmed.

The state's tally of virus cases grew to 69 on Monday night after three women tested positive for COVID-19.

One of the women is a close contact of a known case, another recently arrived from overseas and the third recently travelled aboard a cruise ship.

Mr Gutwein implored people to follow strict social gathering guidelines and stay home.

"Social distancing and abiding by the rules will save your life, it will save your family's life, it will save lives in our community," he said.

© AAP 2020