Launceston Health Hub director Dr Jerome Muir Wilson said the clinic had experienced a 50 per cent increase in bookings for the jab since last week.

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"Up until last week, we had vaccines and not enough bookings. But finally this week, there's been a bit of a swing - which we've put down to the situation in Melbourne," he said.

"I think there were people who were holding off until they thought they needed it, but I think this has been a real wake up call for people."

Federal Health Department data shows there's been a consistent increase in the number of vaccine doses administered through GPs since the primary care rollout commended in March.

Nationally as of May 30, more than 4.24 million people had been vaccinated including 2.36 million through GPs and 345,583 in aged care.

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On Tuesday Premier Peter Gutwein said 100 per cent of Tasmania's aged care homes had received the first dose of the vaccine, 85 per cent a bolster, with all residents expected to be fully vaccinated by the end of next week.

In light of criticisms surrounding Victoria's vaccine rollout, Mr Gutwein said about half of all Tasmania's aged care staff had now received a COVID vaccination.

"We have taken the view that we have responsibility for all Tasmanians and we offered to assist the Commonwealth, they took us up on that offer, and we have been offering vaccinations for our aged care staff in our state-run clinics and also holding outreach clinics where we have been able to," he said.

Last week additional Tasmanian general practices were invited to become vaccine providers.

Dr Muir Wilson said the biggest confusion for patients was if they could access Pfizer if over 50, despite advice that AstraZeneca was safe.

"After discussing it with their GP, if their preference is still Pfizer, then at this stage they need to wait until later this year which puts them at risk of catching COVID in their interim."

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