US President Donald Trump says he wished North Korean leader Kim Jong Un to be healthy when reports surfaced that he may have fallen ill, but declined to comment further.

The president has offered a variety of assessments since reports of North Korean leaders' alleged health problems began to emerge last week.

"I just don't want to comment on it, I don't want to comment on it," he told reporters at the White House when asked if Kim Jong-un still ruled his country.