In a referendum in April, a majority of the island's population voted to end Sunday flights to and from Rarotonga, with those wanting the ban saying Sunday is a sacred day when businesses shouldn't operate.
The prime minister, Henry Puna, called the referendum as part of a campaign promise in the lead-up to a by-election on the island, but has still not said whether he will honour the result.
The corporation's director of destination development, Metua Vaiimene, says the tourism industry is firmly in support of keeping the flights.
He says the government needs to work with the people of Aitutaki to come to a solution.
"We call upon the community in Aitutaki and we call upon the government to engage with the stakeholders in Aitutaki so that this issue can be solved, so that it can be sorted, for the benefit of the community and the benefit of the industry."
Meanwhile, Metua Vaiimene has welcomed an announcement that Jetstar will start flying to Rarotonga in March in a deal which will mean an extra 25,000 return seats to the country every year.
The flights will originate from Sydney or Melbourne, and Australian travellers will connect to Rarotonga via Auckland.
The corporation's director of destination development, Metua Vaiimene, says tourists from New Zealand and Australia are the country's biggest markets, and the new flights will mean more choice and competition.
"It is our largest industry. It's the biggest provider of employment and income here in the Cook Islands. So it's important to continue to invest in that and diversifying the ways in which our visitors can come here, like approaching new airlines such as Jetstar, as part of our overall strategy."
He says the Cook Islands has seen a steady increase in tourism over the last five years, and is expecting about 120,000 visitors this year.