Authorities say an investigation is underway after two staff members of the North West Regional Hospital in Tasmania tested positive for coronavirus.

The hospital is where Tasmania's first death from coronavirus occurred on Monday — a woman in her 80s.

Tasmania COVID-19 snapshot Confirmed cases: 226

Confirmed cases: 226 Deaths: 13, 12 in north-west What do I do if I think I have coronavirus? If you think you might have COVID-19 phone your GP or the Tasmanian Public Health Hotline on 1800 671 738. Need an interpreter? Phone the Translating and Interpreting Service on 131 450 and tell them your language. For more information and factsheets: Visit the Tasmanian Government's coronavirus page here.

In a statement released tonight, the hospital's chief medical officer, Professor Tony Lawler, said he acknowledged the situation "may cause some concern".

"The safety of our patients and our dedicated staff remain our highest priority, and neither the hospital's operations nor patient services have changed at this time," he said.

The two are among six new cases found in the last 24 hours in Tasmania.

Professor Lawler said the Tasmanian Health Service had "moved immediately to establish an Incident Management Team, which will work to ascertain any people who may be at risk of being exposed to coronavirus at the hospital and ensure necessary actions are taken".

"While it may be necessary for other staff and patients to be tested for coronavirus, this will occur as investigations progress.

"We will assess and test any patient or staff member who is determined to be at risk of coronavirus and ensure the highest standards of care continue to be provided at the hospital."

Professor Lawler said patients, staff and the public would be "kept informed of the situation as the investigation progresses".

Earlier, Tasmania's acting director of public health, Dr Scott McKeown, said six new cases of coronavirus had been confirmed in the last 24 hours — two from southern Tasmania, two from northern Tasmania and two from the north-west.