Scott Morrison this week put renewed pressure on states to open up, saying expert medical advice at a national level never recommended shutting internal borders.

"The last time I looked, the prime minister wasn't the director of public health in Tasmania nor was he the premier of Tasmania," Mr Gutwein said on Thursday.

"We'll make decisions that are in the best interests of Tasmania.

"I thank him for his input but at the end of the day, we'll make the call on this when it's right for the state."

Mr Gutwein reiterated he hopes to make a call in July on when the state will reopen.

Mr Morrison on Wednesday said states would have to justify their decisions to stay closed because it wasn't something that came out of the national cabinet and wasn't good for the economy.

"I've got a very good working relationship with the prime minister, who I might add has done an outstanding job," Mr Gutwein said.

"But in terms of borders, that is a matter for me, public health officials and our state emergency controller."

Tasmania shut its borders in mid-March and has since required all non-essential arrivals to quarantine for 14 days.

The state has gone 13 days without a new COVID-19 case, with just eight of 226 recorded infections remaining active.

Health authorities are buoyed by high levels of recent testing, which may pave the way for some internal restrictions to be eased ahead of schedule.

More than 1500 people have been tested in the past two days.

"As more testing occurs and as more negative tests come in, it does give us confidence," Public Health Director Mark Veitch said.

"Everyone wants to enjoy life in more normal fashion but we have to do it safely."

Mr Gutwein has hinted at lifting some restrictions before the Queen's birthday long weekend ahead of a slated shift to stage two in mid-June.

Major tourism drawcard, the Port Arthur Historic Site, has announced it will reopen on July 3 with social distancing measures in place.

Australian Associated Press