WASHINGTON -- US President Donald Trump said Tuesday that he wishes North Korean leader Kim Jong-un well amid reports he may be gravely ill, but refused to comment further.

Trump has offered varying assessments since reports on the North Korean leader's alleged health issues began emerging last week.

"I just don't want to comment on it. I don't want to comment on it. I just wish him well," he told reporters at the White House when asked if Kim is still in control of his country.

Trump did not respond to a question about whether Kim is still alive.

Less than a day earlier, Trump had told reporters that he had a "very good idea" about Kim's current condition but couldn't talk about it yet.

He said the media will "probably be hearing in the not too distant future" before adding: "Nobody knows where he is."

Trump has repeatedly said he hopes the North Korean leader is doing well. But whereas last Tuesday he said the US doesn't know if the reports about Kim's failing health are true, on Thursday he dismissed a CNN report in particular as "incorrect."

The cable network had cited a US official as saying that Washington was looking into intelligence that Kim was in "grave danger" after surgery.

Kim has been out of public view since April 11, when he presided over a Politburo meeting of the ruling Workers' Party.

His absence from an April 15 commemoration of the birthday of his late grandfather, North Korea founder Kim Il-sung, sparked speculation that there may be something wrong with his health.

South Korean officials have insisted there is nothing unusual happening inside the regime.

Trump and Kim have met three times since June 2018 to try to reach a deal on denuclearizing North Korea in exchange for US sanctions relief.

But negotiations have faltered since their second summit in Vietnam in February 2019 ended without a deal due to differences over the scope of their actions.

Last month Trump sent a letter to Kim -- one of a series of missives exchanged between the leaders -- to offer US assistance with COVID-19.

North Korea has at least publicly not accepted the offer while insisting it has no cases of the coronavirus in the country. (Yonhap)