The island state reported 680 new infections on Thursday - the fourth day in a row the daily figure has risen.

Some 60,000 public school students returned to the classroom last Wednesday.

"We have just under 200 public schools. At this stage around half of the schools have reported at least one case. That's going to continue, that's something we should expect," Premier Peter Gutwein said.

Mr Gutwein said national and state public health advice had indicated schools are safe and classrooms are the best place for student learning and their wellbeing.

He said there were 13 outbreaks across public, Catholic and independent schools. Public health defines an outbreak as five or more cases in a classroom setting.

The state's daily case figure, an increase from 625 on Wednesday, is the highest since February 1.

There are 16 people with the virus in hospital, with 11 of those receiving treatment specifically for COVID-19. Two patients are in intensive care.

There are 3266 active cases statewide, a marginal increase on 3116 from 24 hours earlier.

Tasmania has recorded 10 coronavirus deaths since reopening borders on December 15 and a total of 23 since the beginning of the pandemic.

Australian Associated Press