About 35,000 people logged onto the Make Yourself At Home website at 7pm on Wednesday night to secure a voucher to subsidise accommodation or a tourism experience somewhere in Tasmania.

Each of the $5 million in vouchers were allocated in a little over an hour.

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Mr Gutwein said around 20,000 vouchers were issued to benefit around 45,000 people

"The vouchers will underpin our tourism and hospitality sector at a time when it needs underpinning," he said.

"Whilst some people will be frustrated and disappointed, at the end of the day between the two rounds, we will have nearly 90,000 Tasmanians that will be benefitting from the vouchers."

Mr Gutwein would not be drawn on whether there would be a third round of travel vouchers.

"I'm hopeful that I can receive Public Health advice in terms of our border situation and I'll have more to say tomorrow on that," he said.

He said the tourism and hospitality sector would be able to benefit from the movement of people from COVID-safe states once borders reopened.

It is anticipated borders will be open to all states except Victoria and potentially New South Wales.

Labor leader Rebecca White said she hoped that glitches on the website that prevented Tasmanians from accessing a voucher had been fixed.

"There are a number of different ways the government could have distributed vouchers," she said.

"At this rate, they could have provided a voucher for every single Tasmanian in the post given the amount of money that has been spent so far."

She said there continued to be uncertainty over when the borders would reopen.

Ms White said while that uncertainty remained, another round of travel vouchers should be released.