North Korean leader Kim Jong Un is “alive and well”, a top security adviser to the South's President Moon Jae-in said, downplaying rumours over Kim's health following his absence from a key anniversary.

“Our government position is firm,” said Moon's special adviser on national security Moon Chung-in, in an interview with CNN on Sunday. “Kim Jong Un is alive and well.”

The adviser said that Kim had been staying in Wonsan — a resort town in the country's east — since April 13, adding: “No suspicious movements have so far been detected.”

Conjecture about Kim's health has grown since his conspicuous absence from the April 15 celebrations for the birthday of his grandfather Kim Il Sung, the North's founder — the most important day in the country's political calendar.

Kim has not made a public appearance since presiding over a Workers' Party politburo meeting on April 11, and the following day state media reported him inspecting fighter jets at an air defence unit.

His absence unleashed a series of unconfirmed media reports over his condition, which officials in Seoul previously poured cold water on.

“We have nothing to confirm and no special movement has been detected inside North Korea as of now,” the South's presidential office said in a statement last week.

South Korea's unification minister Kim Yeon-chul reiterated on Monday that remained the case, adding the “confident” conclusion was drawn from “a complex process of intelligence gathering and assessment”.

'Grave danger'

Daily NK, an online media outlet run mostly by North Korean defectors, has reported Kim was undergoing treatment after a cardiovascular procedure earlier this month.

Citing an unidentified source inside the country, it said Kim, who is in his mid-30s, had needed urgent treatment due to heavy smoking, obesity and fatigue.

Soon afterwards, CNN reported that Washington was “monitoring intelligence” that Kim was in “grave danger” after undergoing surgery, quoting what it said was an anonymous United States official.

US President Donald Trump on Thursday rejected reports that Kim was ailing but declined to state when he was last in touch with him.

On Monday, the official Rodong Sinmun newspaper reported that Kim had sent a message of thanks to workers on the giant Wonsan Kalma coastal tourism project.

It was the latest in a series of reports in recent days of statements issued or actions taken in Kim's name, although none has carried any pictures of him.

Satellite images reviewed by 38North, a US-based think tank, showed a train probably belonging to Kim at a station in Wonsan last week.

It cautioned that the train's presence did not “indicate anything about his health” but did “lend weight” to reports he was staying on the country's eastern coast.

Reporting from inside the isolated North is notoriously difficult, especially regarding anything to do with its leadership, which is among its most closely guarded secrets.

Previous absences from the public eye on Kim's part have prompted speculation about his health.

In 2014 he dropped out of sight for nearly six weeks before reappearing with a cane. Days later, the South's spy agency said he had undergone surgery to remove a cyst from his ankle.