"We don't think they'll be successful but that is capacity that we face here," Hauenstein said.
Connecting traffic could increase competition for passengers flying to other destinations in the Middle East and Asia.
A variety of other global challenges have cut into Delta's revenue. European sales have been weak due to the weaker Euro, the Paris market is recovering since the terrorist attacks there last November, and there has been a "very small impact" on the Latin American market from cancellations due to the Zika virus.
But all in all, Delta has held onto about half of its savings from fuel costs, according to incoming CEO Ed Bastian. Delta CEO Richard Anderson retires May 2, and Bastian will step up to the chief executive position from his current role as president.
Hauenstein said in a written statement that the airline is "focused on getting unit revenues back to a positive trajectory and we will make adjustments to our fall capacity levels if we are not making sufficient progress over the coming months."
Bastian said the company "will continue to be disciplined with our business in the face of volatile fuel prices," according to a written statement.
Overall, Delta's operating revenue declined 1 percent to $9.25 billion in the first quarter of the year, which ended March 31.
Its operating expense declined 3 percent, including a $1.45 billion decline in adjusted fuel expense.
That contributed to an increase in net income to $946 million from $746 million a year earlier.
The 40 percent decline in market fuel prices helped to lower Delta's fuel costs. But the airline had fuel hedge losses of $118 million and its oil refinery in Trainer, Pa. posted a loss of $28 million in the quarter. Delta has closed its hedge book, but expects to continue to post hedge losses of $200 million per quarter.
Separately, Delta is in the market for narrow-body jets to renew its domestic fleet over the next five years. Among the options, Bastian said, are 737s operated by Delta's Brazilian partner Gol, as that airline looks to trim its operations.