But Coasters need to get in touch with a GP or the Public Health Hotline to request testing.

Health Minister Sarah Courtney said about 100 people a day were being tested but this could be increased.

"We can have up to 500 tests a day and we know that capacity can expand further. We have additional machinery on its way. Thousands of swabs are being deployed to the North-West Coast," Ms Courtney said.

Coronavirus: All the latest updates on COVID-19 for Tasmania

"We can test more but we need people in the community to ring the Public Health Hotline or their GP if they have symptoms.

"If you think it's just a sore throat - think about your family.

"We urge North-West Tasmanians to take up this opportunity."

She said testing had been offered to all staff at the North West Regional Hospital and the North West Private Hospital.

A drive-through testing facility will open at Parkside on Wednesday.

But Greens health spokeswoman Rosalie Woodruff said, rather than waiting for people to self-identify with symptoms, Tasmania needed to start proactively conducting random tests in strategic community settings such as supermarkets.

"This is only way to get a clear picture of the spread of the virus and be proactive with a timely response," Dr Woodruff said.

"Many of the measures the state government has put in place to limit the spread of this virus have been strong and proactive. They must take the same approach to testing in the North-West."

Public Health director Mark Veitch said in most instances tests are taken on one day then transported to the hospital and processed the following day.

"There is an urgent priority to always get in touch with the people who get a positive test and [for them to] learn about that within hours of the test result being completed," Dr Veitch said.

"I can't give a timeline for all the negative tests ... but it is possible it can take an extra day to get though if there's a large volume of tests."

Dr Veitch said it was important people spread out testing appointment throughout the day to reduce any "bottle neck" happening.

He said many were arranging testing between the morning and 3pm but clinics were open until later in the day.

Tasmania has confirmed a total of 165 cases of COVID-19, with 15 cases diagnosed on Tuesday night.

Ms Courtney said all 15 of these cases were associated with the North-West Coast.

Of these 15, nine were healthcare workers, four were patients, one was a close contact of a previous case and one person had been in a number of settings where they could have caught coronavirus but this investigation was ongoing.

Of Tasmania's total cases, 57 people have recovered, 102 cases are active and sadly six people have died.

Ms Courtney said cleaning of the emergency department at the NWRH was underway and it was now expected the it would reopen on Thursday, instead of Wednesday.

The Mersey Community Hospital will not undergo a deep clean yet.

"My current advice is that's not required. If that is required we will take that measure," Ms Courtney said.

Premier Peter Gutwein said measures taken across the state were working in the North and the South, with no positive tests in either region for about a week.

But he urged Tasmanians to not become complacent.

"If you don't think this thing can kill you, think again," Mr Gutwein said.

Mr Gutwein also urged Tasmanians not to take to social media as "keyboard warriors" making negative comments about health workers as the coronavirus pandemic unfolds.

"Let us be kind to each other," Mr Gutwein said.

"Anyone who is thinking of lining up a healthcare worker and taking a pot-shot at them ... draw a breath.

"The only we are going to get to the other side [of these extraordinary circumstances] is if we work together."

Mr Gutwein said staff that had been stood down into quarantine were people who had spent their lives working to support the North-West Coast community.

"Last night I chatted with Emily who was a worker at the NWRH and will be again when the hospital reopens," Mr Gutwein said.

"Emily made the point she was comforted by the fact the government was acting swiftly, comforted by the fact steps were being taken.

"But she explained to me how difficult it was, 11 days ago as one of the first staff to be furloughed, to actually say goodbye to her two young children and her husband as she went into quarantine."

Mr Gutwein said he also wanted to reach out to staff at the Launceston General Hospital to thank them for their efforts during the crisis.