US media reported that Mr Kim was in a fragile condition following surgery.
But in a statement, South Korea's presidential office said no suspicious activity had been detected in their northern neighbour that backed the reports.
US media network CNN cited an anonymous US official who said Mr Kim was in "grave danger" after unspecified surgery in a report on Tuesday.
The Unification Ministry, which deals with inter-Korean affairs, said it could not confirm another report by Daily NK (a news outlet based in South Korea), which quoted another anonymous sources as saying Mr Kim was recovering from heart surgery in the capital Pyongyang and that his condition was improving.
Speculation about Mr Kim's health was raised after he missed a celebration honouring his late grandfather and state founder Kim Il Sung on April 15.
He was last seen four days before that at a government meeting.
Credible information about North Korea and especially its leadership is difficult to obtain.
Even intelligence agencies have been wrong about its inner workings in the past.
CNN quoted Bruce Klingner, a senior research fellow at the Heritage Foundation and former CIA deputy division chief for North Korea, as saying rumours had circulated recently about Mr Kim's health.
"But, over the years, there have been a number of false health rumours about Kim Jong-un, or his father.
"We'll have to wait and see," the network quoted Mr Klingner as saying.