While it is possible that Ms. Sweeney could find employment directing TV programs for Disney, either in the children’s arena or for ABC, she said it was too soon to say exactly how she might make her new career debut.

Image Ms. Sweeney turned down a new contract.

In a separate interview, Mr. Iger declined to say who might take over for Ms. Sweeney, although he said it would be an internal hire. He said an announcement would come sooner than later. “Anne runs a sprawling, important, global division, parts of which are seeing fast-paced change and a fair amount of challenges,” he said. “We fortunately have a deep bench of talented, smart, experienced people.”

Regarding Ms. Sweeney’s decision to leave Disney to pursue directing, Mr. Iger said: “There is nothing below the surface here. I offered her a new multiyear contract, and she came back and said she wanted to do this instead.” He added: “I was somewhat incredulous. I didn’t see that coming.”

Ms. Sweeney, who spent 12 years at Nickelodeon and three years at FX before joining Disney, is known as a highly polished executive with substantial skills in the art of corporate politics. Analysts estimate that her divisions generated $11.9 billion in revenue and $2.6 billion in profit last year.

Her résumé, which is larded with awards, includes helping Disney become the first major TV supplier to join iTunes and building Disney Channel into a juggernaut. She is also credited with turning around ABC’s news division by hiring Ben Sherwood to take it over in 2010. Among other feats, Mr. Sherwood ended the morning dominance that NBC’s “Today” show had for 16 years. ABC’s “Good Morning America” is now the top morning show, raking in the profits that go with that status.

Mr. Sherwood is prominent on the list of possible successors to Ms. Sweeney, along with Nancy Dubuc, the president of the hugely successful A & E Networks. Gary Marsh, president of Disney Channels Worldwide, and Benjamin N. Pyne, president of global distribution for Disney Media Networks, have also been mentioned as contenders.

ABC’s program lineup has not achieved nearly as much success under Ms. Sweeney’s watch as the cable channels, though the network had a period of success starting a decade ago when it introduced three hit shows in one season, “Desperate Housewives,” “Grey’s Anatomy” and “Lost.”