Premier Peter Gutwein said the government had strengthened guidelines for retailers and had asked police to pay special attention to how well those guidelines were followed.

There have been various calls to lock down non-essential retail to help slow the spread of the virus.

"If I am advised by Public Health I should shut down retail, then I would," Mr Gutwein said.

Government requirements of retailers include:

Mr Gutwein defended the state's coronavirus testing record, despite concerns from doctors and the public in March that many people with flu-like or coronavirus-like symptoms were not being tested and/or not being advised to self-isolate.

He said Tasmania had stuck to the national guidelines on testing, and testing was now being expanded to higher risk groups, with GPs to do more.

Asked about statistics suggesting Tasmania had the lowest per capita testing rate of any state, Mr Gutwein said some other states wasted testing reagent early in the piece by testing people who were well and two almost ran out of testing gear.

"If I tested you today and you were negative, unless you isolated yourself away from anyone else for the duration, you could be sick in two weeks," he said.

Tasmania's previously thriving tourism industry has been slugged by the virus and related travel restrictions.

Mr Gutwein believed the industry would pick up once the crisis was past.

"Once the restrictions come off across the country and, I think, across the world, I think people will be hesitant at first to travel, (but) I think there will be a thirst to travel," he said.

"... the Tasmanian tourism product, it won't go bad."

He said the state's wilderness and "iconic" tourism assets would still be there and would still be attractive to people.