The state's vaccination rate is expected to reach 80 per cent in November, Premier Peter Gutwein says.
Mr Gutwein on Wednesday announced the state had reached a significant milestone with 50 per cent of eligible Tasmanians having received their first COVID-19 vaccination dose.
This is ahead of the national vaccination rate of 41 per cent.
Mr Gutwein said 25 per cent of Tasmanians had received their second dose, meaning that one in four eligible Tasmanians were fully vaccinated. "It's important that Tasmanians don't wait, that they vaccinate," he said.
Tasmanian COVID-19 vaccine operations commander Dale Webster said the vaccination program had been going for four months and had recently sped up.
"And we continue to speed up," he said.
The vaccination program opened up to 30 to 39-year-olds this week.
Mr Webster said the program would open up to 12 to 15-year-olds next week with underlying medical conditions or a disability.
He said there were still appointments available this month at state vaccination clinics. Bookings can be made through the government's COVID-19 website.
Mr Webster said Tasmanians had shown a great willingness to embrace the vaccination clinics, adding that 10,000 appointments opened up last Friday with 2000 of those taken up by Sunday.
Mr Webster said the Moderna COVID-19 vaccine was expected to come online in September, pending approval.
He said the AstraZeneca vaccine would be phased out in October as the new vaccine was gradually rolled out.
Mr Webster said state clinics would have the capacity to deliver 15,000 Pfizer vaccinations over this week.
Health Minister Jeremy Rockliff earlier this week warned the state could face short and sharp lockdowns should the highly infectious Delta variant of coronavirus emerge in the state.
Tasmanian Chamber of Commerce and Industry chief executive Michael Bailey has written to the Premier to ask how a lockdown might be managed in Tasmania.
In the letter, he raised the question on whether a lockdown would be confined to regions or statewide and how much notification the business community would receive on such a move.
He questioned which businesses would be deemed essential and what support would be in place for those that were forced to close due to a lockdown.
"We understand the need for the health of Tasmanians to be a priority it we also believe that transparency in these decisions is important," Mr Bailey said.
"South Australia have developed a very simple and publicly available document that outlines their approach to these questions."