SEOUL, South Korea — North Korea’s leader, Kim Jong-un, has received an “excellent” letter from President Trump, the country’s state media said on Sunday, two days after President Xi Jinping of China wrapped up a visit to the North.

After reading the letter, Mr. Kim “said with satisfaction that the letter is of excellent content,” the North’s official Korean Central News Agency reported on Sunday. It added that Mr. Kim appreciated Mr. Trump’s “extraordinary courage,” and that he “would seriously contemplate the interesting content” of the letter.

The news agency carried a photo of Mr. Kim reading the letter in his office. Its brief report provided no further details, including when Mr. Trump’s letter arrived.

Secretary of State Mike Pompeo confirmed the letter on Sunday, expressing hope it could bolster nuclear talks, Reuters reported. “I’m hopeful that this will provide a good foundation” for starting “important discussions with the North Koreans,” he said.