A spokeswoman for Mr. Iger said he was unavailable for an interview.

In recent months, as Disney’s troubles have increased, senior executives have privately pressed Mr. Iger to renew. In its statement on Wednesday, Disney took pains to point out that it was the board, not Mr. Iger, that pushed for an extension. Given his serial contract renewals, a narrative has formed in Hollywood, rightly or wrongly, that he is reluctant to step away from power. “The board determined it is in the best interest of shareholders to extend his tenure, and he has agreed to our request,” Mark G. Parker, chairman of the Disney board, said in the statement, adding that Mr. Iger had already “set Disney on the right strategic path for ongoing value creation.”

Disney shares have been trading at about $90, down 3 percent from a year ago and 54 percent from their peak in March 2021. Following the news of Mr. Iger’s extension, shares remained largely flat in after-hours trading.

The challenge is that, in addition to succession, Disney is dealing with problems on almost every front, including new questions about its movie studios, given disappointing results at the summer box office for “Elemental,” “Indiana Jones and the Dial of Destiny” and, to a lesser extent, “The Little Mermaid.” Disney has been maneuvering to buy full control of Hulu, but such a purchase would be expensive, and Disney is loaded with roughly $45 billion in debt, partly because of the pandemic.

In the meantime, Disney’s earnings engine for the last 30 years — traditional television, including ESPN — has become a shadow of its former self, the result of cord cutting, advertising weakness and rising sports programming costs. Mr. Iger is betting that streaming services will return the company to growth. But Disney+ has been shedding subscribers, and a broader streaming division remains unprofitable, losing nearly $2 billion since the start of the fiscal year.

Disney is also contending with a lingering screenwriters’ strike; and contract negotiations between studios and SAG-AFTRA, the guild that represents about 160,000 actors, have been going poorly and could result in a strike as early as Thursday.