Health Minister Sarah Courtney says requirements for elective surgery were being assessed as the state's hospitals look to increase capacity in preparation for more coronavirus cases.
Two more people had tested positive to the virus over the past three days which brings the total number of confirmed cases in Tasmania to six.
A woman in her 60s tested positive on Saturday night and is in a stable condition at the Royal Hobart Hospital.
She was identified as a close contact of her travel companion, a man in his 60s who has also tested positive to coronavirus.
Ms Courtney said both are tourists to Tasmania.
"All six cases [in Tasmania] are directly linked to people who have arrived in Tasmania from overseas," she said.
"We haven't identified evidence of transmission within our community outside these cases."
She said the Tasmanian Health Service was looking at ways in increase capacity within state hospitals.
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"Without a doubt, coronavirus has the potential to place pressure on our health system so this is why we're working so closely not only within the THS but with the broader primary health care system, aged care and the private hospitals to ensure that we are well-prepared," she said.
"We're at advanced stages of planning around our [intensive care units], our emergency departments and ward capacity."
Ms Courtney said elective surgery requirements would be looked at and re-prioritised if necessary.
"We want to make sure that we have got the maximum capacity available within our system," she said.
Clark independent MHA Madeleine Ogilvie renewed calls on Sunday for the government to tighen its control over the state's borders.
Premier Peter Gutwein dismissed the notion of completely closing them, however.
"In terms of our borders currently, anyone who comes from a high-risk country is placed into self-isolation or quarantined for a period of two weeks," he said.
"We do have I think the unique circumstance where we are an island within an island so I think it's appropriate that we take stronger measures than perhaps other states might take and we're looking at those.
"I won't be shutting our border but what I will be doing is ensuring we manage it to provide a more robust protection to Tasmanians."
Australian Medical Association state representative Helen McCardle on Friday said school closures should be more seriously considered.
"In a small state like ours, it doesn't take much to overwhelm the acute hospital system," she said.
Mr Gutwein said he had received no advice yet on school closures or on an extension of the Easter holiday period for schools.
"If and when we need to close a school based on advice, we will do so," he said.
Mr Gutwein said he didn't believe parents who removed their children from schools due to fear of coronavirus contraction would be penalised.
"I think if a parent felt they wanted to do that for the health and wellbeing of their child, then that would be a matter for the parent," he said.
Labor leader Rebecca White on Sunday said consideration should be given to greater screening of passengers at airports and on the Spirit of Tasmania vessels
She said passengers should have their temperatures taken and their details recorded at least.
Greens health spokeswoman Rosalie Woodruff said the government needed to impose stricter controls over visitors to Tasmania and require all those who arrived to the state by air or sea to self-isolated for 14 days.
She said the government needed to advise Tasmanians to avoid all non-essential travel interstate or overseas.