SEOUL, South Korea — North Korea on Sunday denied President Trump’s assertion that its leader, Kim Jong-un, had sent a letter to him, and suggested that Mr. Trump was using his vaunted relationship with Mr. Kim for “selfish purposes.”

Mr. Trump said the day before during his daily press briefing on the coronavirus that he had received a “nice note” from Mr. Kim.

“I received a nice note from him recently. It was a nice note. I think we’re doing fine,” Mr. Trump told reporters on Saturday at the White House. He also claimed that the United States would have been at war with North Korea had he not been elected and played down the threat of short-range missile tests that North Korea has been conducting since March.

During a phone conversation with President Moon Jae-in of South Korea, Mr. Trump also ​said he had received a “warm letter” from the North Korean leader, Mr. Moon’s aides told reporters on Sunday. But ​later Sunday, ​the North’s Foreign Ministry ​said, “There was no letter addressed recently to the U.S. president by the supreme leadership” of the North.