Tasmania could open its borders to New South Wales residents on November 2.
In naming a date on Monday afternoon, Premier Peter Gutwein said while there were a small number of new cases emerging in the state each day, spread of coronavirus seemed to be contained.
He said monitoring the situation in New South Wales would continue and it was hoped border restrictions would be relaxed from November 2.
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Mr Gutwein said that would be confirmed on Monday at the latest.
He said the state remained on track to lower its borders to residents of Queensland, South Australia, Western Australia, Northern Territory and the ACT next Monday.
A new online registration system for potential travellers will be launched on Friday.
People will be able to access the Tas E-Travel website three days before travel.
The system is intended to help Public Health Service track the origin of people who enter Tasmania
Mr Gutwein said travellers to the state will have to undergo health screening at points of entry to Tasmania.
He said anyone who had symptoms would be required to take a coronavirus test and self-contain until a test result was returned.
Mr Gutwein said it was aimed to open borders to Victoria by December 1, or sooner if circumstances within the state improved.
Public Health director Mark Veitch said it was important for Tasmanians to continue to undergo coronavirus tests now and when borders reopened.
He said certain restrictions might come back into play if coronavirus cases were diagnosed in the state that could not be traced back to a contact.
"I certainly hope we don't have to do that and that should be a pretty powerful motivation for people to follow the rules," Dr Veitch said.
He said there would be no changes on the limit of 20 people attending household gatherings before Grand Final weekend, but suggested this cap would be looked at before Christmas.
Mr Gutwein said the government continued to work with Australian Border Force on a travel bubble between Tasmanian and New Zealand.
He said the Hobart airport could be configured to accept international arrivals in eight to 10 weeks.
"I would hope we would have that arrangement in place with New Zealand sometime in early in the new year," Mr Gutwein said.
"My understanding is that we're getting very close to a decision being made."
Labor leader Rebecca White said Tasmania could not afford to get the process of borders reopening wrong.
"It is also a worry to hear that testing rates are so low," she said.
"The government haven't been doing any advertising encouraging people to get tested.
"You would think a week out from borders reopening that they were really be pushing the message out to Tasmanians to get tested and remind people about how serious this is."
Ms White said there continued to be concerns from the health and aged care sectors that they were not adequately prepared to respond to another coronavirus outbreak in Tasmania.
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