The 20 passengers who landed in Launceston on Monday, on board Virgin flight VA 1464, have been sent SMS messages and email, but remain unaccounted for.

Public Health director Mark Veitch said the contact tracing process for the positive case was well underway and "going well".

Dr Veitch said a person from Scotch Oakburn College who had been identified as a primary contact of the positive Covid-19 case has returned a negative result but remains in quarantine.

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He said there were between 160 to 200 contacts of the positive case, including 100 on the flight on Monday with most of these people already contacted.

"There was a small number of people in that group, about 20, who we were embarking upon further calls this morning. Sometimes it is difficult t o catch up with people on the flights, either the wrong number or out of contact range, so we are working with other colleagues and agencies so we can see where those remaining people are," Dr Veitch said.

"My message is, if you were on flight VA 1364 from Melbourne to Launceston on Monday, and haven't yet been contacted directly by phone, by Public Health, please call the hotline on 1800 671 738."

Meanwhile, Covid-19 testing in Tasmania has set a new record.

In the last 48 hours up until Friday morning there have been more than 3400 tests carried out across the state, including 1643 tests in the past 24 hours.

A further 1189 people had made appointments for testing by noon on Friday, including 266 across the Launceston clinics and 617 in the south.

Hundreds of appointments are still available, including 200 at Launceston's Wellington South clinic, and 85 at the Prospect mobile testing clinic.

The Wellington South clinic will remain open until 9 pm on Friday and Saturday night, and the Prospect mobile clinic will be open until 5 pm.