The chief executive of Tourism Cook Islands, Chris Wong, says the country's air links to North America are vital, bringing in up to 28,000 visitors every year.
Air New Zealand says its three connecting flights to Los Angeles are under review but no decision has been made.
In a general statement, it says the airline is not able to subsidise unprofitable routes.
Mr Wong says if Air New Zealand deems the route unprofitable, they would want to see facts and figures.
"And if need be, from our side, look at how we could change that. We have got to think outside of the box a little here because you are talking about the economy of a country here, it is not just restricted to the three services."
Chris Wong says one matter they would want on the table is making the route from Rarotonga to Los Angeles direct by dropping the stop-over in Papeete.