Premier Peter Gutwein said the schools included five public, four Catholic and three independent, spread across the north and south of the state.

An outbreak is defined by Public Health as five cases in a single learning environment within a week, and students or teachers who test positive must isolate at home.

It was an increase on the seven reported on Tuesday.

Mr Gutwein said the term "outbreak" could be misleading, despite it being a Public Health definition.

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"I want to reset this conversation about schools just a little bit," he said.

"We have 12 schools that have had cases that have met the public health definition of an outbreak, but to be clear, those cases are no longer in the schools.

"They were tested, and children stay at home. With the commentary that we have an outbreak in a school, that couldn't be further from the truth.

"We have a number of cases that meet the definition that Public Health have set, but those cases are tested and those children are at home, they're not at school."

The identity of the schools was not disclosed.

Tasmania reported 625 new cases on Wednesday morning, a fourth straight day in which case numbers have increased. They had dropped to 371 on Sunday.

The government had been eager to foreshadow such an increase for when schools returned, pointing to increasing testing requirements and more movement of people.

The number of people in intensive care with COVID increased from one to two, and there are 13 in hospital, eight of whom are being treated primarily for COVID.

There are about 850 eligible people left in Tasmania without any form of vaccination, Mr Gutwein said, as the first dose rate for people aged 16 and above reached 99.18 per cent.

About 96.15 per cent of Tasmanians aged 12 and over are fully vaccinated, and 60.65 per cent of children aged five to 11 have received one dose.

Just under 50 per cent of eligible people have received their booster.

Tasmania is also likely to require only minimal support from the Australian Defence Force in aged care homes.

Three facilities requested assistance, but Mr Gutwein said it appeared likely that two of those would no longer have outbreaks by Friday when ADF personnel are expected to arrive.

"What's really positive is that there won't be support for three facilities - one has definitely moved out of its outbreak phase - and there's a possibility that a second will move out of its outbreak phase as well, and so the ADF support that will be provided will be minimal, probably around five people supporting one facility," he said.