There is no need for Tasmanians to race out and stock up on goods because of the situation with COVID-19 interstate, Premier Peter Gutwein says.
This week Victoria moved to stage 4 restrictions which saw the shutdown of many businesses and a curfew imposed in Melbourne.
"The Port of Melbourne remains open. It is essential and continues to operate fully," Mr Gutwein said.
"In terms of supply lines and in terms of freight, we've been assured those supply lines will remain open.
"There is no reason for anyone to be concerned."
Mr Gutwein said if businesses pick up on any supply issues, they should contact the Business Tasmania Hotline on 1800 440 026.
"At this time, I'm not aware of any matters that have been raised or any challenges coming out of the Victorian situation but it is early days," Mr Gutwein said.
"They are in the fight of their life and I want to extend my thoughts, and the thoughts of the Tasmanian government, to Victoria."
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He said Tasmanians should not inform themselves about the state's COVID-19 situation by looking at Victoria.
"What they will see being reported now, they will be anxious," he said.
"The most important thing we can do now is be responsible for ourselves and ensure we do social distancing, we follow good hand hygiene and we follow the rules."
Tasmania remains COVID-19 free.
About 71,000 tests have been conducted with 700 carried out on Tuesday.
State Controller Darren Hine said more than 30 people had been charged with breaching their quarantine requirements to date.
"Generally, people have been doing the right thing," Commissioner Hine said.
"We have had some breaches unfortunately and we do continue to carry out compliance checks.
"We've always had about 1000 people in home quarantine. They are checked by public health with a phone call to see if they are feeling well and we've also checked them from a policing point of view."