Tasmania is now testing at a higher rate per population than the Australian average, and more than Victoria, Western Australia, Queensland, the ACT and the Northern Territory.
The up to 1000 tests per day currently being undertaken will be doubled to 2000, after a delivery of equipment from the federal government and the Minderoo Foundation.
On Friday, 600 tests were completed with two-thirds being from the North-West.
Anyone in the state with symptoms such as a cough, sore throat or runny nose is encouraged to call the Public Health Hotline on 1800 671 738.
Director of Public Health Mark Veitch said the North-West outbreak was believed to be under control.
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He said a confirmed case at the Mersey Hospital was believed to have been first acquired in early to mid-April, and appropriate contact tracing and quarantining was underway.
Extensive testing around a cluster of nine cases based in Smithton has not uncovered any more confirmed cases.
And as of Sunday, 14 days have passed since the last infection at the Melaleuca aged care home in East Devonport, meaning the facility can resume the same operations as the rest of the state.
However, Premier Peter Gutwein said there would inevitably be more cases of the virus uncovered as the state ramps up testing.
"We will see further cases of coronavirus, as we will see in other states and territories across the country," he said.
"What that [will] demonstrate is that the increased testing that we're doing is doing exactly what we want it to do, which is to find where the virus is so that we can get on top of it and so that we can stamp it out."
He stressed that the restrictions lifted on the North-West Coast from Monday were only the additional restrictions imposed in response to the outbreak: for example the closing of large stores.
"The North-West Coast will go back to the same level of restrictions, and the social distancing that applies, around the rest of the state," he said.
"What that means is you should still stay home. You should only leave your home if you want to go out for essential supplies, medical services; if you need to go to school, to work or to volunteer."
There were no new cases of coronavirus in Tasmania on Friday.