The first COVID-19 vaccinations will be administered from the Launceston General Hospital and North West Regional Hospital on March 15.
Vaccinations will be available at the Mersey Community Hospital for staff on March 19.
Health Department secretary Kathrine Morgan-Wicks said 1168 people from the first priority group had been vaccinated in the second week at the Royal Hobart Hospital clinic.
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Overall, 2327 people have been vaccinated since the vaccine was received.
Ms Morgan-Wicks said 578 staff and residents have been vaccinated at aged care and disability care facilities.
Premier Peter Gutwein said 6720 doses of AstraZeneca COVID vaccine would be soon received and would be dispensed at first from the Royal Hobart Hospital and the Roy Fagan Centre.
He said more details on how to arrange bookings for vaccinations will be made available next week.
Mr Gutwein said the number of clinics administering the vaccine would increase as the number of vials received by the state increased.
The second priority group under the vaccination rollout will be brought forward to March 19.
People in this group include:
- people aged over 70 years old;
- health care workers;
- Aboriginal and Torres Strait Islander people;
- young adults with particular medical conditions or a disability;
- and people working in high-risk areas like defence, police, fire, emergency services and meat processing.