"These are reports that came out (about his illness). We don't know. We don't know. Though I have had a very good relationship with him. I can only say I wish him well. If he is in the kind of condition that the reports say, then it is a very serious condition," Trump said at a daily briefing on Tuesday.
This comes after a US intelligence official had said that North Korea's leader is in grave danger following surgery this month.
On April 15, Kim absence at his grandfather's birthday celebration had raised speculation about his well-being. He had been seen four days before that at a government meeting, according to intelligence reports cited by CNN.
Meanwhile, South Korea had responded by saying that it has seen no unusual signs suggesting that North Korean leader is ill, government officials said on Tuesday.
"There is nothing unusual going on in North Korea. It's not true," a government official was quoted as saying by Yonhap News Agency.
Presidential spokesperson Kang Min-seok also said that nothing unusual has been detected in North Korea.
"No unusual signs have been identified inside North Korea. There is nothing we can confirm with regard to Chairman Kim's alleged health problem," Kang was quoted as saying.
Kim's absences from official state media often spark speculation and rumours about his health. North Korea has no free press and is often a black hole when it comes to the country's leadership. Analysts are heavily reliant on scanning state media dispatches and watching propaganda videos for any semblance of a clue.
Kim last appeared in North Korean state media on April 11. April 15 -- North Korea's most important holiday, is the anniversary of the birth of the country's founding father, Kim Il Sung.
( With inputs from ANI )