Donald Trump is believed to have been contacted by North Korea’s supreme leader on Friday. It comes after Mr Trump announced that he and his wife, Melania Trump, tested positive for COVID-19 late on Thursday evening.
One of Mr Trump’s close advisers, Hope Hicks, also tested positive for the virus on Friday before the president’s announcement.
President Trump has been flown to a military hospital after the White House confirmed he was feeling “lethargic”.
North Korean media reported that Mr Kim said: “I have come across unexpected news that you and your commander have been tested positive for the coronavirus.”
The message continued: “I [send] consolation to you and your family.
“I sincerely wish you and your commander a complete recovery as soon as possible.”
Mr Kim added: “You will surely get over it. Warm greetings to you and the commander.”
Mr Trump announced the news of his positive coronavirus test on Twitter.
He wrote late on Thursday evening: “Tonight, @FLOTUS and I tested positive for COVID-19.
“We will begin our quarantine and recovery process immediately. We will get through this TOGETHER!”
On Friday, the White House confirmed that the president had been taken to the Walter Reed National Military Medical Centre in Maryland.
He is set to spend a “few days” at the hospital after receiving advice from his medical team.
Kayleigh McEnany, Mr Trump’s press secretary, said that despite the president experiencing “mild symptoms” he has remained in “good spirits”.
She added: “Out of an abundance of caution, and at the recommendation of his physician and medical experts, the President will be working from the presidential offices at Walter Reed for the next few days.
“President Trump appreciates the outpouring of support for both he and the First Lady.”
In a video tweeted by the president, he said: “I want to thank everybody for the tremendous support.
“I’m going to Walter Reed hospital. I think I’m doing very well but we’re going to make sure that things work out.
“The First Lady is doing very well. So thank you very much I appreciate it, I will never forget thank you.”
Mr Trump is believed to be suffering with a mild fever.
His doctor said he “remains fatigued” but is in “good spirits”.
Mr Trump has reportedly been injected with an experimental antibody cocktail of drugs and has taken vitamins and an aspirin.
The news of Mr Trump’s positive coronavirus test came just a month before the US presidential election is set to take place.
President Trump is also scheduled to appear in his second election debate against his competitor Joe Biden in less than two weeks.
It is not clear yet how his coronavirus diagnosis may affect the US presidential election.