Tasmania is banning travellers from coronavirus "hotspots" in Queensland, including venues frequented by several women who allegedly returned to the state illegally.
It was announced on Friday the hotspots would be added to a banned list which already includes all of Victoria and virus-hit regions of NSW.
People from those areas are only allowed in under exceptional circumstances.
Premier Peter Gutwein implored people to do the right thing when filling out border documents.
"If you don't tell the truth, we will catch you and we will throw the book at you," he told reporters.
Two cases of community transmission have been linked to the women, who have been charged with providing false or misleading documents.
Public Health Director Mark Veitch confirmed venues they visited would be added to the banned list.
Tasmania has regained its virus-free status after the recovery of a young woman who returned from Victoria and tested positive while in hotel quarantine on July 20.
Mr Gutwein outlined further conditions around the state's reopening to South Australia, Western Australia and the Northern Territory on August 7.
Tasmanians heading to South Australia won't be able to enter the state via Melbourne, with the SA government forcing those arrivals to quarantine.
Some business groups have called for borders to stay closed and internal restrictions to be further eased, considering the island state is virus-free.
But Dr Veitch said social distancing and gathering rules would stay in place for months regardless of the border situation.
"We can't expect to go back to freely mixing as if COVID doesn't exist. At some case a coronavirus case will occur," he said.
"If you drop a case of coronavirus into a setting where people are crowded and mixing, you have a real risk of an explosive outbreak.
Mr Gutwein said Tasmanians in Victoria should think twice about coming home given the mainland state's outbreak.
Tasmania remains closed to non-essential travellers from Queensland, NSW and the ACT, with Mr Gutwein to provide an update on August 7.