The infection of two further health care workers with COVID-19 is being described by the public health authority as a "very serious" incident and a possible expansion of the testing regime in the North-West has consequently been flagged.
It follows the diagnosis of an emergency department worker at the Mersey Community Hospital late last week.
Coronavirus: All the latest updates on COVID-19 for Tasmania
On Friday night, six new cases of coronavirus were confirmed in Tasmania, with two of those being staff at the North West Regional Hospital. It brings the state's total confirmed cases to 80.
Health Minister Sarah Courtney said on Saturday that the two individuals worked on the medical ward.
Two of the other cases had been linked to overseas travel, one is from interstate and the other was a passenger on the Ruby Princess cruise ship.
Ms Courtney said an incident management team, being led by the NWRH's chief medical officer Tony Lawler, had been established to respond to and control the fallout from the hospital cases.
She stressed that the two workers had been in - and continue to be in - self-isolation and that the priority for the incident management team was to identify potential close contacts of the cases, including their colleagues and patients.
"Everything is being done to manage and resolve this situation as quickly as possible," the minister said.
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"At this stage, hospital operation and service delivery [at the NWRH] remains unchanged.
"My thoughts are with the staff.
"I know that they will be working very hard."
The newly established incident management team at the hospital will be investigating any possible sources of infection "within the health care setting", according to Public Health acting director Scott McKeown.
"It's far too early to say where [the cases'] source of infection came from," Dr McKeown said.
"I need to stress that this investigation is to ensure the safety of patients, staff at the facility and people in the North-West region."
Dr McKeown said it was possible the testing regime could be further expanded in the North-West as a result of the two new cases coming off the back of the Mersey case.
The state's first coronavirus-related death was recorded at the NWRH on Monday. The second Tasmanian death was confirmed at the Royal Hobart Hospital on the following day.
It's far too early to say where [the cases'] source of infection came from.Scott McKeown, Public Health acting director
Labor leader Rebecca White said the Opposition would continue to call on the government to "dramatically ramp up" testing in the state.
"This is the only way we can get an accurate picture of whether the virus is spreading through the community," she said.
"Despite assurances that testing criteria have been relaxed, we are still hearing reports of people who are symptomatic being denied tests.
"Concerningly this includes medical professionals."
Ms White said the government needed also to outline how long it was taking to process tests.
"Labor is aware of delays of up to four days which makes contact tracing more difficult," she said.
Deputy Premier Jeremy Rockliff acknowledged the efforts of frontline health staff, saying they did an "amazing" job.
"We know we best support you by staying at home," he said. "And that is why we, as a government, reinforce this as an absolute priority."
"To the North-West community, who will no doubt have concerns after hearing two of its NWRH staff have tested positive, there is an immediate investigation underway."
Meanwhile, Dr McKeown said the Tasmanian Health Service's investigation into two COVID-19 cases in the Devonport area, which have given rise to concerns that community transmission could be occurring in the region, was nearing its conclusion.
One of the cases subject to investigation is that of the Mersey worker.
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