Virgin Australia shares remained steady despite the airline earlier announcing it was to cut all international flights and cut domestic capacity by 50 per cent.
Prime Minister Scott Morrison has lifted the country's travel ban to a level four, the highest, advising Australians not to leave the country.
The Federal government has announced that $715 million in fees and industry levies for Australian airlines will be waived in a relief package aimed to help them through major hits to tourism from global COVID-19 travel bans.
Qantas shares held remarkably firm on Tuesday despite the airline announcing it was to cut international capacity by 90 per cent earlier in the day.
Qantas and Jetstar will cut 90 per cent of international capacity and 60 per cent of domestic until the end of May.
Virgin and Qantas shares avoided a nosedive on Monday despite one of the toughest weekends the aviation industry has seen.