Health Minister Sarah Courtney on Tuesday announced birthing services would return to the North-West Coast.
She said intensive care services and radiation therapy had already returned to the North-West Regional Hospital.
Coronavirus: All the latest updates on COVID-19 for Tasmania
Ms Courtney said surgical wards and paediatric services would reopen later this week.
Ms Courtney said presentations to respiratory clinics remained strong with 122 in the North, 203 in the South, and 224 across the North-West.
"If you have any kind of respiratory symptoms, a bit of a sore throat, a cough, a sniffly nose, please come and get tested," she said.
In other news:
International travel between Australia and New Zealand will be discussed at Tuesday's national cabinet meeting.
New Zealand Prime Minister will attend the meeting.
Premier Peter Gutwein cautioned the idea of a trans-Tasman travel bubble would not necessarily mean a return to unrestricted visitation between the two countries.
He said he had recently been in discussion with Tourism Tasmania and Hobart Airport on the prospect of direct flights between Tasmania and New Zealand.
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