(Redesign, written with comments from the CEO of Qantas and Virgin)

DOHA, June 19 (Reuters) – Qantas Airways and Virgin Australia have seen no decline in domestic bookings due to rising inflation and interest rates, but fares need to rise to help them recover some of the cost of high oil prices, their chief executives said on Sunday.

Australia’s two biggest airlines are operating domestic capacity above pre-pandemic levels as demand rebounds, but Qantas has cut some flights for July and August to try to raise fares and may take more action, said said its chief executive on the sidelines of an industry conference in Doha.

“We are seeing very strong international demand across the board and that is helping us restore oil prices to the international market,” Qantas chief executive Alan Joyce told reporters. “In the domestic market, we may need a little less capacity in the market to get that recovery and we’re working on that right now.”

Virgin Australia chief executive Jayne Hrdlicka said her airline had made two fare increases but was more wary of cutting capacity before it hit its 33 per cent domestic market share target, especially when demand was strong.

“Most months we have 33% revenue share, but not quite 33% capacity share,” she told Reuters in an interview. “We will carefully balance a combination of capacity management and price increases.”

Virgin Australia was bought by US private equity firm Bain Capital in 2020 and is no longer listed on the stock exchange.

Hrdlicka said it returned to profit in April and an IPO was likely as early as 2023, but the timing would depend on market conditions.

“Stock markets, as you know, are not in great shape right now,” she said. “So it will just depend on when there is a good opportunity from a market perspective.” (Reporting by Jamie Freed, editing by Louise Heavens and Barbara Lewis)