Donald Trump has 'very good idea' about Kim Jong-un's health, but refuses to speak about it

US President Donald Trump has a "very good idea" of North Korean leader Kim Jong-un's condition, but is refusing to elaborate.

Mystery is swirling about the dictator's status after rumours began last week that he may be dead or in a critical condition following a cardiovascular procedure. Kim hasn't been seen recently and on April 15 missed his late grandfather's birthday celebrations, the Asian state's most important holiday.

Daily NK, a speciality website run mostly by North Korean defectors, first reported the leader had undergone a procedure, before CNN's chief national security correspondent Jim Sciutto reported Kim was in "grave danger". The rumours were further fuelled by a Reuters report saying Chinese medical professionals were heading to North Korea.

South Korea has rejected the claims, saying Kim was "alive and well".

But speculation has been sparked again, however, when Trump was asked on Tuesday if he had an update on Kim's health.

"Yes, I do have a very good idea, but I can't talk about it now," he said.

"I just wish him well. I have had a very good relationship with Kim Jong-un."

Trump went on to claim that if he wasn't President the United States would be at war with North Korea before saying "I hope he is fine".

"I do know how he is doing, relatively speaking. We will see. You will probably be hearing in the not-too-distant future."

On Monday (US time), CNN reported that a letter had been sent from Kim to South African President Cyril Ramaphosa dated April 27. However, CNN said there is no way of independently verifying the letter's authenticity.

Photos were published on Monday appearing to show Kim's train outside his Wonson holiday complex. 

There have long been concerns about Kim's health as he is known to be a heavy smoker and overweight.