Walt Disney Co. Chief Executive Robert Iger gave investors a preview of what he wants his company’s next chapter to be.

After several years of assuaging investors nervous about cord-cutting and competition from streaming giants such as Netflix Inc., Mr. Iger, on a conference call with Wall Street analysts Tuesday, focused on Disney’s high-stakes plan to fight back: the company’s own direct-to-consumer offerings and a pending $71.3 billion acquisition of 21st Century Fox Inc.’s entertainment assets.

“Consumers...