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The South Korean government cast doubt Tuesday on rumors that North Korean dictator Kim Jong Un was gravely ill, but U.S. officials said he may be incapacitated after heart surgery.

Speculation about Kim's health has mounted after he failed to attend his late grandfather's birthday celebrations on April 15, the most important date in North Korea's calendar, known as "Day of the Sun."

The rumors accelerated Tuesday when the South Korean website Daily NK cited one unnamed source as saying Kim, who is believed to be 36, had undergone heart surgery and was recuperating in a villa outside the capital Pyongyang.

Several U.S. officials told NBC News that U.S. intelligence reporting indicates that Kim recently had cardiovascular surgery and has been out of public view for days. Some officials said the intelligence suggests Kim may be incapacitated. U.S. intelligence and agencies and the military are working to figure out his health status, officials said.

As a result of the rumors, South Korean financial markets took a dip and its currency weakened against the dollar.

A TV screen at a railway station in Seoul, South Korea, shows file footage of Kim during a news broadcast Tuesday. Jung Yeon-je / AFP - Getty Images

But later on Tuesday the office of South Korean President Moon Jae-in denied that Kim was ill, saying that it could confirm he was at work and "currently touring provincial areas with his close aides."

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The office said it had no "evidence to support speculation about his ill health."

North Korea is one of the most secretive nations on earth and events inside the country are often difficult or impossible to verify. But South Korea and its intelligence agencies often have solid information about what goes on inside its authoritarian neighbor.

In China, which is North Korea's biggest but uneasy ally, the foreign ministry said it is aware of the reports but did not know their source, according to spokesman Geng Shuang.

Kim is the latest in his family's dynasty to rule North Korea's repressive regime, which is responsible for some of the world's worst human-rights atrocities, according to defectors and international watchdogs.

But because Kim has no clear successor, if he died it might risk instability at the top of this nuclear-capable country, with ramifications far beyond its own population of 25 million.

North Korea has built an increasingly sophisticated nuclear and ballistic missile program under Kim, according to monitoring groups. And although a 2018 summit between Kim and President Donald Trump produced an agreement that Trump claimed would lead to denuclearization, negotiations have since stalled.

Though relatively young, Kim appears obese in photographs. He has been pictured smoking and his former sushi chef has said he is a heavy drinker.

Speculation about his health began after he missed celebrations for his grandfather's birthday on April 15, one of the most important events in the North Korean calendar.

It's not the first time such an absence has fueled rumors about Kim. In 2014 he was absent from public view for a month and was pictured walking with a cane when he finally re-emerged. South Korea's spy agency later said that Kim had a cyst removed from his ankle.

Kim's grandfather was Kim Il Sung, who founded the North Korea state in 1948, and his father was Kim Jong Il, the country's previous leader, who died in 2011.

"When Kim Jong Il died, U.S. intel didn't know for two days," said Bruce Klingner, a former CIA analyst covering North Korea, now a senior research fellow at the Heritage Foundation, a conservative Washington think tank. "North Korea is the hardest of hard targets," he added, referring to the difficulty getting reliable information on events inside the country.

Some Korea-watchers have speculated that his younger sister, Kim Yo Jong, might be in the running to be a future leader.

She has enjoyed a meteoric rise in recent years, representing her brother at the 2018 Winter Olympics in Pyeongchang, and issuing statements praising the United States and denouncing South Korea respectively.