A conference call to discuss Walt Disney Co. ’s financial results Tuesday became a forceful defense of ESPN in an age of cable cord-cutting, reflecting Wall Street’s concerns about the future of one of the media world’s most lucrative brands.

While granting that sports powerhouse ESPN has experienced “some subscriber losses” that he declined to specify, Disney Chief Executive Robert Iger repeatedly said the channel will remain in a healthy position thanks to its long-term rights to the NBA, college football playoffs and other programming, as well as the value to advertisers of its programming that is largely watched live.

The combination, Mr. Iger said in his opening remarks, “adds up to a very strong hand and gives us enormous confidence in ESPN’s future no matter how technology transforms the media business.”

Still, as consumers shift to less costly “skinny packages” or abandon cable altogether, Disney is feeling the impact. The company previously said its cable business, primarily driven by ESPN, would achieve “high single digit” operating income growth on a compound basis between fiscal 2013 and 2016.

But partly because of lower subscriber levels, that figure will end up in the “mid-single digits,” said Chief Financial Officer Christine McCarthy. The strong U.S. dollar also had an impact, Ms. McCarthy added.