The Latest: Trump says Korea talks 'going along very well'

In this May 26, 2018, photo provided on May 27, 2018, by the North Korean government, North Korean leader Kim Jong Un, left, and South Korean President Moon Jae-in, right, shake hands after their meeting at the northern side of Panmunjom in North Korea. The content of this image is as provided and cannot be independently verified. Korean language watermark on image as provided by source reads: "KCNA" which is the abbreviation for Korean Central News Agency. (Korean Central News Agency/Korea News Service via AP)
In this May 26, 2018 photo provided on May 27, 2018, by South Korea Presidential Blue House via Yonhap News Agency, North Korean leader Kim Jong Un, right, and South Korean President Moon Jae-in, left, reach out to shake hands before their meeting at the northern side of Panmunjom in North Korea. Kim and Moon met Saturday, May 26, for the second time in a month, exchanging a huge bear hug and broad smiles in a surprise summit at a border village to discuss Kim's potential meeting with U.S. President Donald Trump and ways to follow through on the peace initiatives of the rivals' earlier summit. (South Korea Presidential Blue House/Yonhap via AP)
In this May 26, 2018 photo provided on May 27, 2018, by South Korea Presidential Blue House via Yonhap News Agency, South Korean President Moon Jae-in, left, is guided by North Korean leader Kim Jong Un, right, at the northern side of Panmunjom in North Korea. Kim and Moon met Saturday, May 26, for the second time in a month, exchanging a huge bear hug and broad smiles in a surprise summit at a border village to discuss Kim's potential meeting with U.S. President Donald Trump and ways to follow through on the peace initiatives of the rivals' earlier summit.(South Korea Presidential Blue House/Yonhap via AP)
In this May 26, 2018, photo provided on May 27, 2018, by the North Korean government, North Korean leader Kim Jong Un, left, and South Korean President Moon Jae-in, right, walk together to their meeting at the northern side of Panmunjom in North Korea. The content of this image is as provided and cannot be independently verified. Korean language watermark on image as provided by source reads: "KCNA" which is the abbreviation for Korean Central News Agency. (Korean Central News Agency/Korea News Service via AP)
In this May 26, 2018 photo provided on May 27, 2018, by South Korea Presidential Blue House via Yonhap News Agency, North Korean leader Kim Jong Un, left, and South Korean President Moon Jae-in, right, shake hands after their meeting at the northern side of Panmunjom in North Korea. Kim and Moon met Saturday, May 26, for the second time in a month, exchanging a huge bear hug and broad smiles in a surprise summit at a border village to discuss Kim's potential meeting with U.S. President Donald Trump and ways to follow through on the peace initiatives of the rivals' earlier summit. (South Korea Presidential Blue House/Yonhap via AP)
In this May 26, 2018 photo provided on May 27, 2018, by South Korea Presidential Blue House via Yonhap News Agency, North Korean leader Kim Jong Un and South Korean President Moon Jae-in attend their meeting at the northern side of Panmunjom in North Korea. Kim and Moon met Saturday, May 26, for the second time in a month, exchanging a huge bear hug and broad smiles in a surprise summit at a border village to discuss Kim's potential meeting with U.S. President Donald Trump and ways to follow through on the peace initiatives of the rivals' earlier summit. (South Korea Presidential Blue House/Yonhap via AP)
In this May 26, 2018 photo provided on May 27, 2018, by South Korea Presidential Blue House via Yonhap News Agency, South Korean President Moon Jae-in, right, is guided by North Korean leader Kim Jong Un, left, at the northern side of Panmunjom in North Korea. Kim and Moon met Saturday, May 26, for the second time in a month, exchanging a huge bear hug and broad smiles in a surprise summit at a border village to discuss Kim's potential meeting with U.S. President Donald Trump and ways to follow through on the peace initiatives of the rivals' earlier summit.(South Korea Presidential Blue House/Yonhap via AP)
In this May 26, 2018 photo provided on May 27, 2018, by South Korea Presidential Blue House via Yonhap News Agency, North Korean leader Kim Jong Un, center left, and South Korean President Moon Jae-in, right, walk after their meeting at the northern side of Panmunjom in North Korea. Kim and Moon met Saturday, May 26, for the second time in a month, exchanging a huge bear hug and broad smiles in a surprise summit at a border village to discuss Kim's potential meeting with U.S. President Donald Trump and ways to follow through on the peace initiatives of the rivals' earlier summit. (South Korea Presidential Blue House/Yonhap via AP)
In this May 26, 2018 photo provided on May 27, 2018, by South Korea Presidential Blue House via Yonhap News Agency, North Korean leader Kim Jong Un, right, and South Korean President Moon Jae-in, left, shake hands before their meeting at the northern side of Panmunjom in North Korea. Kim and Moon met Saturday, May 26, for the second time in a month, exchanging a huge bear hug and broad smiles in a surprise summit at a border village to discuss Kim's potential meeting with U.S. President Donald Trump and ways to follow through on the peace initiatives of the rivals' earlier summit. (South Korea Presidential Blue House/Yonhap via AP)
In this May 26, 2018 photo provided on May 27, 2018, by South Korea Presidential Blue House via Yonhap News Agency, South Korean President Moon Jae-in writes on a visitor's book as North Korean leader Kim Jong Un, left, stands at the northern side of Panmunjom in North Korea. Kim and Moon met Saturday, May 26 for the second time in a month, exchanging a huge bear hug and broad smiles in a surprise summit at a border village to discuss Kim's potential meeting with U.S. President Donald Trump and ways to follow through on the peace initiatives of the rivals' earlier summit. (South Korea Presidential Blue House/Yonhap via AP)

SEOUL, South Korea — The Latest on diplomatic efforts involving the Koreas (all times local):

10:25 a.m.

President Donald Trump says negotiations over a potential summit with the leader of North Korea are "going along very well."

Trump told reporters Saturday that: "We're doing very well in terms of the summit with North Korea," adding that "there are meetings going on as we speak."

Trump said they are still considering June 12 in Singapore for the summit with Kim Jong Un. He said there is a "lot of good will" and denuclearization of the Korean peninsula would be "a great thing."

Trump also said that talks between North Korean leader Kim Jong Un and South Korean President Moon Jae-in have "gone very well."

___

10:20 a.m.

South Korea's president says North Korean leader Kim Jong Un remains committed to holding a summit with President Donald Trump and to the "complete denuclearization of the Korean Peninsula."

South Korean President Moon Jae-in met Kim at the border on Saturday for the second time in a month to discuss how to keep Kim's summit with Trump on a track. The Kim-Moon meeting followed a whirlwind 24 hours that saw Trump cancel the highly anticipated June 12 meeting before saying it's potentially back on.

Moon told reporters Sunday that Kim reaffirmed his denuclearization commitment and told Moon he's willing to cooperate to end confrontation for the sake of the successful North Korea-U.S. summit.

Moon says his meeting with Kim was arranged at Kim's request.

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