Under Kim's rule since 2011, North Korea has expanded its arsenal of nuclear weapons and long-range missiles, and with no obvious successor, any change in leadership in the secretive, authoritarian state would raise concerns about instability that could impact other North Asian countries and the United States.
Speculation about Kim's health erupted after his unprecedented absence from April 15 celebrations to mark the birthday of his late grandfather and North Korea's founder, Kim Il Sung.
South Korean Unification Minister Kim Yeon-chul, who oversees engagement with North Korea, said it was plausible Kim that decided against attending due to the coronavirus, given stringent steps his government has taken to head off an outbreak.
"He had never missed the anniversary for Kim Il Sung's birthday since he took power, but many anniversary events including celebrations and a banquet had been canceled because of coronavirus concerns," the minister told a parliamentary hearing.
"I don't think that's particularly unusual given the current (coronavirus) situation," the minister said, although North Korea has said it has no confirmed cases of the coronavirus.
An authoritative source familiar with US intelligence assessments said credible reports to the US government suggested the reason Kim's presidential train had been spotted near a presidential retreat at the resort of Wonsan last week was that Kim had been staying there to avoid catching the virus.
US government experts lacked categorical evidence to prove this, but were for the most part dismissing media reports suggesting that Kim had contracted some kind of serious illness, the source said.
Kim Yeon-chul described reports that Kim had undergone a heart procedure, and that a Chinese medical team had traveled to North Korea, as "fake news."
A US official, who spoke on condition of anonymity, said Washington's view was largely in line with the South Korean minister's assessment.
US President Donald Trump said on Monday he has a good idea of how Kim Jong Un is doing and hopes he is fine, but would not elaborate.
On Tuesday, Trump was asked by a reporter about these comments and whether he thought Kim was still in control of North Korea and replied: "I don't want to comment on it. I just wish him well."
Trump has met Kim three times in an attempt to persuade him to give up a nuclear weapons program that threatens the United States as well as its Asian neighbors. While talks have stalled, Trump has continued to hail Kim as a friend.
TRAIN AND BOAT WATCHING
The South Korean minister noted that there had been at least two instances since mid-January when Kim Jong Un had not been seen in public for nearly 20 days.
The last time official media in North Korea reported on Kim's whereabouts was when he presided over a meeting on April 11, but there have been near-daily reports of him sending letters and diplomatic messages.
South Korean officials have said they have detected no unusual movements in North Korea and have cautioned against reports that Kim may be ill.
Washington-based North Korea monitoring project 38 North said on Saturday satellite images from last week showed a special train that was probably Kim's at Wonsan, lending weight to reports he had been spending time in the resort area.
On Tuesday, the website NK News said leisure boats often used by Kim off the coast of Wonsan had been active throughout this month, indicating his likely continued presence in the area.
Reuters reported on Saturday that China had dispatched a team to North Korea, including medical experts to advise on Kim Jong Un, though it was unclear what the trip signaled in terms of his health.
Japanese Prime Minister Shinzo Abe said he was paying close attention to developments.
North Korea has responded to the global coronavirus pandemic by canceling some large events and imposing a border lockdown and quarantine measures.
If Kim Jong Un is hiding out due to fears surrounding COVID-19, it would "puncture a hole in the state media narrative of how this crisis has been perfectly managed," said Chad O'Carroll, CEO of Korea Risk Group, which monitors North Korea."If he is merely trying to avoid infection, it should theoretically be very easy to release photos or videos of a healthy looking Kim," he said.