Washington (AFP) - US President Donald Trump wished North Korea's Kim Jong Un "well" on Tuesday but stopped short of directly commenting on the reclusive leader's health amid reports he underwent surgery.

"I can only say this: I wish him well," Trump told reporters at the White House, noting the "good relationship" he shares with the North Korean leader.

"I just hope he's doing fine," Trump said, adding he "may" reach out to Kim to see how he is doing.

"If he is in the kind of condition that the reports say, that the news is saying, it's a very serious condition."

Trump declined to say whether he had direct information about Kim's health, and suggested he was basing his information on news reports.

"I don't know that the reports are true," he said.

The US president's comments follow a flurry of questions about Kim's health after a report Tuesday that Kim was being treated after surgery.

South Korea has played down the report, which followed mounting speculation over Kim's absence from a key anniversary.

Pyongyang marked the birthday of its late founder, Kim's grandfather Kim Il Sung, on April 15 -- by far the most important date in its annual political calendar. Kim was not seen in attendance.

Daily NK, an online media outlet run mostly by North Korean defectors, said Kim underwent a cardiovascular procedure earlier this month and was recovering at a villa in North Phyongan province.

"Excessive smoking, obesity and fatigue were the direct causes of Kim's urgent cardiovascular treatment," it cited an unidentified source inside the country as saying.

CNN, citing an anonymous US official, said Washington was "monitoring intelligence" that Kim was in "grave danger" after undergoing surgery.

In a statement, a spokesman for the South's presidential Blue House said: "We have nothing to confirm and no special movement has been detected inside North Korea as of now."

Trump and Kim have held two summits, beginning June 2018 in Singapore, which was the first ever face-to-face meeting between leaders of the two countries.

The summit focused on security and denuclearization issues, but subsequent talks between the two leaders collapsed in Hanoi, Vietnam in 2019.