By Gabriel Araujo

RIO DE JANEIRO, June 6 (Reuters) - Brazilian airline Azul AZUL3.SA is stepping up capacity cuts amid higher jet fuel prices linked to the Iran war, and the carrier will continue to trim flying to protect cash in an uncertain environment, CEO John Rodgerson said.

Rodgerson told Reuters the industry's largest companies were reducing capacity to better align with demand at higher cost levels, and Azul would follow suit, going beyond earlier cuts as the conflict drags on.

"When we made our initial cuts, we thought the war would be over by now," he said in an interview on Friday, in the build-up to a meeting of global airline chiefs in Rio de Janeiro.

"But it's continuing, so we're going to continue to opportunistically cut some frequencies, make sure that we're only flying things that make sense."

Most of Azul's reductions in the second quarter were on international routes, with further adjustments focused on domestic frequencies rather than pulling entire cities, Rodgerson said.

"Do you fly to Curitiba six times a day? Maybe with these fuel prices, it should be four." The airline was prioritizing its main hubs in Campinas, Belo Horizonte and Recife, he added.

"We're yet to pull cities, but that's always on the table. But you first start with utilization and cutting frequencies.

"You don't want to be utilizing an aircraft 13, 14 hours a day when fuel prices double."

Rodgerson said Azul's balance sheet after a major debt restructuring put it in a stronger position than some peers to adapt. It exited Chapter 11 proceedings in February with backing from United Airlines UAL.O and American Airlines AAL.O.

Azul expects pricing to remain under pressure in the seasonally weaker second quarter, but sees scope for higher fares to stick as demand strengthens into the third and fourth quarters, he said.