Premier Peter Gutwein announced the move on Monday afternoon after a national cabinet meeting.

The federal government is in charge of vaccinating aged care and disability staff across Australia, but the national program is expected to soon undergo a "reset".

Mr Gutwein said the state's government decision to take control of administering the vaccines was not a concession that something had gone wrong.

"We've got capacity to assist, so we're assisting," he told reporters.

"In terms of the Commonwealth rollout across the state to (aged care) residents, that is running on track. It had a slow start but it is running well and truly as it should."

Almost 55,000 Tasmanians, about 11 per cent of the state's adult population, have been vaccinated against COVID-19.

It is the highest proportion of any state or territory.

State Deputy Health Secretary Dale Webster said the 12,000 workers are expected to receive their jabs by the end of July and Tasmania's overall rollout wouldn't be pushed back.

"It's about which groups we should prioritise going forward," he said.

Mr Gutwein said the state department of health would be in touch with aged care and disability facilities once a timeline was ironed out.

Australian Associated Press