SEOUL, South Korea • North Korean and U.S. officials are holding “behind-the-scenes talks” to arrange a third summit between President Donald Trump and North Korean leader Kim Jong Un on the fate of the North’s expanding nuclear arsenal, South Korea’s president said, four months after a second meeting between the leaders in Vietnam collapsed without any agreement.

There have been no public meetings between Washington and Pyongyang since the breakdown of the Vietnam summit. But the prospects for a resumption of U.S.-North Korea diplomacy have brightened since Trump and Kim recently exchanged personal letters. Trump called Kim’s letter “beautiful” while Kim described Trump’s as “excellent,” though the contents of their letters have not been disclosed.

Trump was asked Wednesday as he departed for Asia if he would be meeting with Kim at the Group of 20 summit in Japan.

Trump said he wouldn’t be meeting with Kim, but then added: “I may be speaking with him in a different forum. I will be going, as you know, to South Korea after the summit.” He didn’t elaborate.

In a response Tuesday to questions by The Associated Press and six other news agencies, South Korean President Moon Jae-in said that Trump’s and Kim’s “willingness to engage in dialogue has never faded” and that their recent letter exchanges prove that.

Moon, a liberal who met Kim three times last year, has made dialogue with the North as a means to forging peace on the Korean Peninsula a centerpiece of his presidency. He has played a central role in facilitating U.S.-North Korean negotiations, even if those efforts have at times been overshadowed by the Trump-Kim talks that he helped broker.

Moon said he doesn’t see the Vietnam summit as a failure. He said he thinks the meeting served as a chance for Washington and Pyongyang to better understand each other’s positions and “put everything they want on the negotiating table.”

“The success of denuclearization and the peace process on the Korean Peninsula cannot be determined by a summit or two,” Moon said, adding that the discussions in Vietnam will form the basis for future talks. “Both sides clearly understand the necessity for dialogue,” he added.

Despite the deadlocked nuclear negotiations, both Trump and Kim have described their personal relationship as good. When asked whether Kim’s recent letter included a mention about another summit, Trump said, “Maybe there was.”

“But we, you know, at some point, we’ll do that,” Trump said.

“Getting along very well. He’s not doing nuclear testing,” he said.

FILE — In this Feb. 28, 2019, file photo, U.S. President Donald Trump and North Korean leader Kim Jong Un take a walk after their first meeting at the Sofitel Legend Metropole Hanoi hotel, in Hanoi, Vietnam. South Korea’s president Moon Jae-in on Tuesday, June 25, 2019, said North Korean and U.S. officials are holding “behind-the-scenes talks” to set up a third summit between the countries’ leaders. (AP Photo/Evan Vucci, File)

Evan Vucci