The Latest: Koreas agree to hold military, Red Cross talks

South Korean Unification Minister Cho Myoung-gyon, center, speaks to the media before leaving for the border village of Panmunjom to attend South and North Korea meeting, at the Office of the South Korea-North Korea Dialogue in Seoul, South Korea, Friday, June 1, 2018. (AP Photo/Ahn Young-joon)
The head of North Korean delegation Ri Son Gwon, second left in front, arrives to meet with South Korean Unification Minister Cho Myoung-gyon at the southern side of Panmunjom in the Demilitarized Zone, South Korea, Friday, June 1, 2018. North and South Korea on Friday resumed senior-level peace talks Seoul sees as an important step in building trust with Pyongyang amid a U.S.-led diplomatic push to persuade the North to give up its nuclear weapons. (Korea Pool/Yonhap via AP)
South Korean Unification Minister Cho Myoung-gyon, center, speaks to the media before leaving for the border village of Panmunjom to attend South and North Korea meeting, at the Office of the South Korea-North Korea Dialogue in Seoul, South Korea, Friday, June 1, 2018. (AP Photo/Ahn Young-joon)
South Korean Unification Minister Cho Myoung-gyon, left, shakes hands with the head of North Korean delegation Ri Son Gwon during their meeting inside the Peace House at the southern side of Panmunjom in the Demilitarized Zone, South Korea, Friday, June 1, 2018. North and South Korea on Friday resumed senior-level peace talks Seoul sees as an important step in building trust with Pyongyang amid a U.S.-led diplomatic push to persuade the North to give up its nuclear weapons. (Korea Pool/Yonhap via AP)
South Korean Unification Minister Cho Myoung-gyon, right, leaves for the border village of Panmunjom to attend South and North Korea meeting, at the Office of the South Korea-North Korea Dialogue in Seoul, South Korea, Friday, June 1, 2018. (AP Photo/Ahn Young-joon)
South Korean Unification Minister Cho Myoung-gyon, right, and the head of North Korean delegation Ri Son Gwon arrive to hold their meeting inside the Peace House at the southern side of Panmunjom in the Demilitarized Zone, South Korea, Friday, June 1, 2018. North and South Korea on Friday resumed senior-level peace talks Seoul sees as an important step in building trust with Pyongyang amid a U.S.-led diplomatic push to persuade the North to give up its nuclear weapons. (Korea Pool/Yonhap via AP)
South Korean Unification Minister Cho Myoung-gyon, right, shakes hands with the head of North Korean delegation Ri Son Gwon during their meeting inside the Peace House at the southern side of Panmunjom in the Demilitarized Zone, South Korea, Friday, June 1, 2018. North and South Korea on Friday resumed senior-level peace talks Seoul sees as an important step in building trust with Pyongyang amid a U.S.-led diplomatic push to persuade the North to give up its nuclear weapons. (Korea Pool/Yonhap via AP)
South Korean Unification Minister Cho Myoung-gyon, second from left, talks with the head of North Korean delegation Ri Son Gwon, second right, during their meeting inside the Peace House at the southern side of Panmunjom in the Demilitarized Zone, South Korea, Friday, June 1, 2018. North and South Korea on Friday resumed senior-level peace talks Seoul sees as an important step in building trust with Pyongyang amid a U.S.-led diplomatic push to persuade the North to give up its nuclear weapons. (Korea Pool/Yonhap via AP)
South Korean Unification Minister Cho Myoung-gyon, second from right, shakes hands with the head of North Korean delegation Ri Son Gwon during their meeting inside the Peace House at the southern side of Panmunjom in the Demilitarized Zone, South Korea, Friday, June 1, 2018. North and South Korea on Friday resumed senior-level peace talks Seoul sees as an important step in building trust with Pyongyang amid a U.S.-led diplomatic push to persuade the North to give up its nuclear weapons. (Korea Pool/Yonhap via AP)
South Korean Unification Minister Cho Myoung-gyon, left, shakes hands with the head of North Korean delegation Ri Son Gwon before their meeting inside the Peace House at the southern side of Panmunjom in the Demilitarized Zone, South Korea, Friday, June 1, 2018. North and South Korea on Friday resumed senior-level peace talks Seoul sees as an important step in building trust with Pyongyang amid a U.S.-led diplomatic push to persuade the North to give up its nuclear weapons. (Korea Pool/Yonhap via AP)

SEOUL, South Korea — The Latest on talks between North and South Korea (all times local):

6 p.m.

North and South Korea have agreed to hold military and Red Cross talks later this month on reducing tensions and resuming reunions of families separated by the 1950-53 Korean War.

The rivals also agreed at a meeting of senior officials at the border village of Panmunjom to soon establish a liaison office at the North Korean border town of Kaesong and hold sports talks on fielding combined teams in some sports at the Asian Games in August, as they continue to take steps toward reconciliation.

South Korea says building trust with North Korea is crucial amid a U.S.-led diplomatic push to persuade the North to give up its nuclear weapons.

The high-level meeting between the Koreas followed talks in New York between U.S. Secretary of State Mike Pompeo and senior North Korean envoy Kim Yong Chol on a possible summit between President Donald Trump and North Korean leader Kim Jong Un. American delegations are also meeting with North Koreans at Panmunjom and in Singapore.

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