A top U.S. general on Wednesday said he assumes that Kim Jong Un is still “in full control” of North Korea’s nuclear and military forces, amid reports that the regime’s leader is facing serious health issues.

Vice Chairman of the Joint Chiefs of Staff Gen. John Hyten said he has “no reason not to assume” that Kim Jong Un is still in control of the country.

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“I assume Kim Jong Un is still in full control of the Korean nuclear force and the Korean military forces,” Hyten told reporters Wednesday, noting that the Pentagon has not received any intelligence to suggest otherwise.

Hyten’s comments come after reports that Kim was in poor health after a cardiovascular procedure.

While his condition is unclear, a well-placed defense intelligence source told Fox News on Tuesday that the U.S. government has extensive plans in place for when Kim eventually is gone, taking into account all the complications that could arise from his eventual death.

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The official described the likelihood of a huge humanitarian crisis within North Korea that could include millions of people facing starvation and a mass exodus of North Korean refugees into China. Intelligence sources told Fox News that part of the plan would be to rely heavily on China to step in and help manage the situation on the ground inside North Korea, partly due to China's proximity and partly due to logistical challenges of the U.S. providing humanitarian assistance.

The Daily NK -- an online news periodical based in Seoul, which is run mostly by North Korean defectors -- has reported that Kim, 36, was recovering from his April 12 surgery at a villa. The report, translated from Korean to English, said Kim has been in bad health because of "heavy smoking, obesity and overwork."

But specifics on Kim's condition remain unclear, as North Korea has been notorious for withholding and distorting news inside its borders.

South Korean officials downplayed the implications of these reports, noting no unusual activity in North Korea.

South Korea’s Yonhap News Agency, in response to the reports, said “it’s not true” and there was “no specific trend.”

“We have no information to confirm regarding rumors about Chairman Kim Jong Un’s health issue that have been reported by some media outlets,” South Korean presidential spokesman Kang Min-seok said. “Also, no unusual developments have been detected inside North Korea.”

Speculation often surfaces about North Korea’s leadership based on attendance at important state events. An intelligence source told Fox News on Monday that there have been suspicions that Kim was unwell since April 15 after he did not attend North Korea’s most important holiday, the birthday of his grandfather Kim II Sung.

North Korea’s Korean Central News Agency (KCNA) has claimed Kim presided over a meeting on April 11 discussing coronavirus prevention and electing his sister as an alternate member of the political bureau of the ruling Workers’ Party. State media have since reported that Kim also sent greetings to Syrian President Bashar al-Assad and Cuban President Miguel Díaz-Canel, as well as “birthday spreads” to two North Korean officials and a new centenarian.

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Meanwhile, sources told Fox News that the White House is aware of the reports of Kim's health, but there has been no confirmation of his condition. Talks between President Trump and Kim over North Korea’s nuclear program have been long stalled. One source noted that during their last summit, foreigners who were in proximity to Kim noted unusually heavy breathing for someone his age.

The president on Tuesday was asked about reports of Kim’s health and said there was no confirmation.

"Well, these are reports that came out, and we don't know. We don't know," Trump said Tuesday during the White House coronavirus task force briefing. ”I've had a very good relationship with him. ... You know, I can only say this -- I wish him well. Because if he is in the kind of condition that the reports say... that's a very serious condition.

"But I wish him well," he continued. "We've had a good relationship. I've said it. I've said it many times. If somebody else were in this position, we would have been, right now, at war with North Korea. And we're not at war. And we're nowhere close to war with North Korea."

It’s unclear what would happen with the regime if Kim is sidelined by health problems or dies.

While North Korea has not made clear who would potentially succeed Kim, some experts believe his sister, Kim Yo Jong, would step in as leader, at least during a transitional period.

Others believe North Korea could be ruled by the collective leadership of ruling party elites, similar to the post-Joseph Stalin Soviet Union.

Fox News' Ben Florance, Lucas Tomlinson, Gillian Turner and John Roberts contributed to this report, as well as The Associated Press.