The new cases were announced on Sunday night, but Premier Peter Gutwein only confirmed they were linked to the North West Regional Hospital in Burnie this morning.
Three other cases have previously been linked to the hospital.
The two new cases include a health worker and a patient.
“An investigation is under way, which will obviously include the identification of contacts both in the community and within the hospital,” Gutwein said this morning.
“It will look at the risk to staff, patients and visitors to the hospital.
“I want to, very clearly, say that we will aggressively track and trace contacts and in terms of the incident management teams that have been established they will do everything they possibly can to get to the bottom of this.”
Another two cases confirmed overnight brings the state’s total to 86.
The two other cases were linked to travel on the Ruby Princess cruise ship and contact with a known coronavirus case.
