Nintendo Co. has had only two presidents in its modern era—Hiroshi Yamauchi from 1949 to 2002 and Satoru Iwata from 2002 until Saturday, when he died of cancer. Speculation about who comes next centers on Shigeru Miyamoto, 62, the creator of such franchises as Donkey Kong, Mario and Zelda.

Mr. Miyamoto is known for his wide circle of friends including Japanese filmmaker Hayao Miyazaki and rock musician Paul McCartney. And he has been helping to nurture younger talent at Nintendo after years spent designing some of Nintendo’s popular games.

"I am surprised at this sudden news and overcome with sadness," Mr. Miyamoto said in a statement issued through the company on Monday. He said he would maintain the game-development stance that he and Mr. Iwata established and work with developers to create the kind of future successes that the late president would have wanted.

In an interview with The Wall Street Journal’s Sarah E. Needleman at the Electronic Entertainment Expo in June, Mr. Miyamoto said he often assigns teams to carry out ideas from him and younger employees. As an example, he pointed to the new shooter game “Splatoon,” which was released for Wii U in May and has already sold more than a million copies globally.

“At the senior level, we supported them,” Mr. Miyamoto said through a translator. “So that’s how we are transitioning.”

Nintendo said it has no plans yet for who would replace Mr. Iwata, who was 55 and also held the position of representative director. The company didn’t name an interim president but said that the company’s two remaining representative directors—Mr. Miyamoto and Genyo Takeda—would continue in that position.

Mr. Takeda, a 66-year-old engineer, comes from the hardware side of the company and has been responsible for consoles including the Nintendo 64.

Mr. Iwata was active until days before his death and was leading the company’s effort to cope with the rapid spread of smartphone games.

Faced with the sluggish performance of its flagship Wii U console and handheld 3Ds devices, Nintendo has recently been stepping out of its comfort zone by preparing smartphone games and licensing its characters for the theme-park business.

Nintendo is scheduled to unveil its first game for smartphones by the end of this year and give details next year about its next-generation NX game console. A Nintendo spokeswoman said there were no schedule changes planned for these initiatives despite Mr. Iwata’s death.