TOKYO—Nintendo Co. President Satoru Iwata has died of cancer at age 55, the company said Monday, putting the company’s leadership in question just months before it embarks on its first foray into mobile gaming.

Mr. Iwata had been president since 2002 and led the introduction of successful products such as the Wii console. But in recent years, the company’s share price and market presence lagged behind with the rise of games on smartphones, a trend which Mr. Iwata was long reluctant to join.

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