Qantas started flying from Sydney to Nadi four times a week in January, and now plans to introduce daily flights over the Christmas-New Year period.
Qantas also operates a codeshare agreement with Fiji Airways, and owns a 46-percent stake in the airline.
The chief executive of Fiji Airways, Andre Viljoen, said Australian visitor numbers to Fiji were flat and Qantas' expansion made little sense.
Fiji Airways does not have the capacity to compete with Qantas and the expansion could damage the carrier and the people whose livelihoods depend on it, Mr Viljoen said.
Qantas said the expansion would boost visitor numbers, ultimately supporting the Fiji economy.