This comes after the second confirmed case of coronavirus in Tasmania failed to heed a warning by health authorities to self-isolate while awaiting his test results when he went to two nightclubs and to work at a busy Hobart hotel.

The man in his 20s returned a positive test to the virus in late on Saturday and is now in a satisfactory condition at the Royal Hobart Hospital.

But on Friday the man attended Cargo and Obar nightclubs between 10pm and 2am and worked as a food and beverage attendant at a conference at the Grand Chancellor Hotel on Saturday.

Last week a 40-year-old man in Launceston, who was the state's first case of the virus, also failed to follow self-quarantine instructions when he visited a city supermarket.

Health Minister Sarah Courtney said the Hobart man's failure to comply with directions to self-isolate between being tested for the virus and receiving his results was unacceptable.

READ MORE: Hobart coronavirus case did not self-isolate

Ms Courtney said she had sought further advice from the Department of Public Health about additional steps needed to ensure people comply with self-isolation.

"I send a very strong message to Tasmanians: if you have been asked to be in self-isolation you must comply with that," Ms Courtney said.

"It is very serious and it's very irresponsible if you do not comply with self-isolation."

Public Health director Dr Mark Veitch said there were options within the Public Health Act to prosecute people who put others at risk.

"There are penalties and charges but we want to move towards making sure people understand what they need to do [so] they have no reason not to be compliant," Dr Veitch said.

Greens health spokeswoman Rosalie Woodruff said Tasmanians, particularly rural Tasmanians, needed clear and direct advice as to how they could self-isolate.

"We are concerned there is not enough direct information, particularly for people in rural and regional Tasmania, about how they will be able to get food and other services if they are asked to self-isolate," Dr Woodruff said.

"People are trying to imagine a situation where they have been asked to self-isolate, possibly with their whole family, and they are trying to think ahead to be prepared for this situation."

Dr Woodruff said health authorities needed to get to the bottom of why the man in Hobart did not self-isolate when asked to.

"Was it a lack of support, was it a lack of understanding or was it a lack of will?" Dr Woodruff said.

Franklin Labor MHA David O'Byrne said coronavirus was an added complication to a health system already in crisis.

Mr O'Byrne said he wanted to know what the government would be doing to support health workers and regional Tasmanians.

"We know more needs to be done to support workers and to help the system respond, not only to day-to-day pressures, but also any impact by the coronavirus," Mr O'Byrne said.

Tasmania escalated its response to the virus to level two on Friday.

Ms Courtney said the state was well-prepared for a range of scenarios.

"And depending on how many more cases we have, those scenarios will be enacted," she said.

"I'm confident we have a plan that's able to cover all Tasmanians, no matter what your circumstances are or where you live."

A total of 114 tests have been completed in Tasmania returning two positive results.

If you are displaying symptoms of coronavirus, please contact the Public Health Hotline on 1800 671 738.