Premier Peter Gutwein has set a target of 90 per cent double vaccination by December 1 to give Tasmanians the opportunity for an "open" Christmas and summer.
Tasmania passed 50 per cent double dose vaccinated on Wednesday, and 69 per cent first dose.
Public Health authorities expect to reach 70 per cent double dose by early-to-mid October.
As an interim target, Mr Gutwein wants the state to reach 80 per cent double dose vaccinated by Melbourne Cup Day - November 2.
Mr Gutwein said it was "a race" against other states, and he encouraged Tasmanians to work together to win it.
He said on current trends, the state could reach 90 per cent by the start of summer - December 1 - while other states would only be around the 80 per cent mark.
"We can open up with confidence during December, so that we're open for Christmas and for summer," Mr Gutwein said.
"I've asked the vaccination team to continue to lift the pace of the rollout."
At that stage, and under the National Plan, Tasmania could consider opening up to other states.
Mr Gutwein said the coming weeks ahead "will be our most important", as the state prepares "to live with COVID".
He raised the prospects of greater freedoms for vaccinated Tasmanians.
"By being vaccinated, you'll have more access to travel, you'll have more access to events, to venues, to certain jobs, and importantly you'll have less chance of catching COVID and importantly, much less chance of being seriously ill," he said.
"Being double vaccinated is access to life in a COVID environment."
'Ambitious' target can be met, Health secretary says
Vaccination rates across all age cohorts in Tasmania indicate the state should be able to meet the summer target, Health Department secretary Kathrine Morgan-Wicks believes.
Over 91 per cent of over-70s have received their first dose, 84 per cent of over-60s, and 67 per cent of those aged 30 to 59.
About 45 per cent of those aged 16 to 29 have had their first dose, and 32 per cent of 16-19-year-olds.
Since becoming eligible on Monday, 5000 Tasmanians aged 12 to 15 have booked in to appointments, have 4.8 per cent have already received their first dose.
Ms Morgan-Wicks said these rates indicated a willingness to get vaccinated.
"We know that we can achieve 90 per cent as we are already hitting very high levels of vaccination in the majority of our age cohorts," she said.
"If Tasmanians keep booking in for vaccination at these same rates as the last five weeks, and showing up for their appointment, we will hit our goal of 90 per cent vaccinated."
In Tasmania, 7104 of the 7383 residential aged care workers have received at least one dose, and 5910 of those are fully vaccinated. It leaves 202 unvaccinated and 67 with a medical exemption from the mandatory vaccination requirement, who are not counted in the unvaccinated figure.
Public Health director Mark Veitch said there would come a time when COVID would enter the state, and it was up to authorities to determine when Tasmania would be in a vaccination position to cope with it.
"COVID is going to come into Tasmania in the months to come," Dr Veitch said.
From today, Tasmanians aged 60 and above will have access to the Pfizer and Moderna vaccines.
The Moderna vaccine will be available in pharmacies for anybody aged over 12, with more than 50 pharmacies expected to have access from the start of October.
From Saturday morning, masks will be required at indoor and outdoor events with more than 1000 people.
The Premier also announced a home quarantine trial for Tasmanians returning from regional NSW.
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