President Trump sent Kim Jong-un a letter, the White House said Sunday, saying it’s part of “ongoing” correspondence between the leaders as they seek a possible third summit to reel in North Korea’s nuclear ambitions.

Press Secretary Sarah Sanders did not divulge the contents of the letter in a brief statement, though Mr. Trump has been boasting about a warm letter he received from the North Korean strongman weeks ago. That letter appeared to mark the first anniversary of their 2018 summit in Singapore.

The correspondence signals increased dialog ahead of Mr. Trump’s trip to the G20 summit in Japan and a stop in Seoul to meet with South Korean President Moon Jae-in, who has tied much of his legacy to the Korean peace process.

The North Korean Central News Agency characterized Mr. Trump’s letter as “excellent.”

“After reading the letter, the Supreme Leader of the Party, the state and the armed forces said with satisfaction that the letter is of excellent content,” the state-run agency said. “Appreciating the political judging faculty and extraordinary courage of President Trump, Kim Jong-un said that he would seriously contemplate the interesting content.”

Public diplomacy between the leaders had stalled since February, when a second summit between Mr. Trump and Mr. Kim was abruptly cut short after the two sides failed to strike a far-reaching deal to end the North’s nuclear and missile programs.

Mr. Trump said at the time that he had to walk away from Hanoi because the North Koreans demanded sweeping sanctions relief in exchange for only a limited commitment to destroy part of their nuclear arsenal, a characterization Pyongyang later challenged.

North Korea accused the administration of being “gangster-like” in its demands for firm concessions, prior to sanctions relief.

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