Any traveller entering Tasmania who lies about where they have been will be punished, Premier Peter Gutwein has warned.
This comes after three women were charged after allegedly lying on a border declaration form when entering Queensland after travelling from Victoria.
Mr Gutwein urged people entering Tasmania to be absolutely truthful about where they had been and what their circumstances were.
"If you lie and you are caught out, we will throw the book at you," he said.
"I would say to all Australians, the rules that have been put in place are there to protect you and the people that you love.
"What we are seeing occurring across the country should be opportunity to pause and reflect that we are in a good place but we need to do everything that we can - what's occurring in other states could happen here."
Mr Gutwein will give an update on the state's borders situation on Friday but a final decision on if Tasmania will open to Queensland, New South Wales and the ACT will not be made until August 7.
[NSW] has still got transmission and unfortunately Queensland has a small number of cases, and we will be watching very closely what happens there," he said.
"What's occurring in Queensland at the moment is one of the reasons why we took the very cautious steps that we did last week when we announced we would not be opening to the eastern seaboard.
"This underlines the cautious, sensible approach we will take.
"We have one of the safest places in the planet here and I want to keep it that way."
When asked if protocols for travellers coming from Victoria would tightened, Mr Gutwein said as he had previously indicated mandatory testing of any essential worker coming out of Victoria would commence on Friday.
"There are only a very small number of people that would fit that category and that's on the basis those skills are not available anywhere else in the country, to save lives or are skills crucial to our economy."