SEOUL, South Korea — There was one state event that the secretive leader of North Korea, Kim Jong-un, never missed: a visit to the Kumsusan Palace of the Sun every April 15 to mark the birthday of his grandfather, the founder of the dynastic regime. In the mausoleum, both his grandfather and his father lie in state.

So when Mr. Kim was a no-show at this year’s anniversary in Pyongyang, it triggered speculation about his whereabouts and even his health. Such rumors gained further traction after Daily NK, a Seoul-based website relying on anonymous sources inside the North, reported Monday that Mr. Kim was recovering from heart surgery performed on April 12.

By Tuesday, South Korean officials were questioning the accuracy of the report. Kang Min-seok, a spokesman for President Moon Jae-in, said South Korea “has so far detected no special signs inside North Korea,” a stock phrase often used to cast doubt on unsubstantiated news reports.

[Update: South Korea confident that rumors of Kim Jong-un illness are wrong.]

North Korea also tried to dispel the speculation. On Tuesday, its official news agency said Mr. Kim had sent birthday gifts to exemplary workers and a birthday letter to the Cuban president on Monday.