Premier Peter Gutwein has warned a second stage of stronger isolation measures to contain the spread of coronavirus in Tasmania could be imposed over the coming days.
In his daily address to media on Tuesday morning, he said movement to a "hard lockdown" was being contemplated.
Coronavirus: All the latest updates on COVID-19 for Tasmania
"We will move to harder measures if we have to," Mr Gutwein said.
Tasmanian hospitality businesses have borne the brunt of business trading restrictions imposed by the federal government on Sunday night.
The move has resulted in tens of thousands of job losses around the state.
Mr Gutwein said he felt for those who were now out of work.
"It breaks my heart that we had to take the measures we had to yesterday," he said.
"To all those people who lost their jobs, I'm so very, very sorry."
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Mr Gutwein said police compliance teams would operate from today to ensure businesses abided by restrictions and people under self-isolation requirements did so.
There were six new cases of coronavirus cases identified on Monday.
Five of the cases were cruise ship passengers and one was a returned traveller
Of the cruise ship passengers, four were from the Ruby Princess and one from the Celebrity Solstice.
Mr Gutwein said Sports Minister Jane Howlett was now in self-isolation.
He said Ms Howlett's chief of staff had been contacted by Queensland Health and told to self-isolate as he had been in close contact with someone infected with coronavirus.
The pair had recently travelled to Townsville for a sports conference.
Mr Gutwein paid tribute to the work of frontline workers in health, education and police in his morning address.
"I want to especially recognise our health professionals today," he said.
"You have my respect and admiration and the respect and admiration of the government."