Labor has called for mandatory immediate coronavirus testing of all arrivals in Tasmania, for them to be quarantined until the test outcome is confirmed, then retested at 12 days.
Tasmania's testing regime for arrivals is less strict than South Australia and Western Australia, where these measures have been in place.
In Tasmania, people granted quarantine exemption are able to attend workplaces and move within hotels while awaiting the outcome of their coronavirus test, Labor has claimed.
Only individuals from Victoria and other areas considered "hot spots" are subject to mandatory testing upon arrival in Tasmania.
Labor leader Rebecca White said without greater controls on the movement of people entering Tasmania with quarantine exemptions, it placed the state at greater risk.
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"Public health advice has convinced the government not to open the borders to anywhere in the country, that should give the government reason to test everybody coming into Tasmania for COVID because they've obviously got public health advice that's concerning enough to make them feel that no state or territory is safe," she said.
"What WA and SA have done is they've introduced mandatory testing for all arrivals into their state from Victoria and other hot spots on arrival and then on day 12 of their quarantine.
"That's because it can take some time for the virus to present, but also, people are mingling in hotels. They're joining together in exercise yards, they're taking smoking breaks together."
The government has not released figures on how many people are still entering Tasmania, but data showed the type of professions granted an exemption from quarantine before May 15, when the virus was present in the state.
Since then, further restrictions have been applied to prioritise "specialist services and skills from other states before Victoria or designated hot spots".
When asked about Labor's suggestion for greater testing of arrivals, State Growth Minister Michael Ferguson said he did not trust Labor.
"If we were following Rebecca White's advice on border control, Tasmania right now would be a suburb of Melbourne," he said.
Mr Ferguson said border controls were "strict enough" already.
"We've been operating in a way - including testing and business continuity and separation of business units - so that even if a business were to have experienced an infection that they could've isolated it, tracked and traced, and ensured that other parts of the business weren't affected," he said.
The Department of Health was contacted for comment.