The rivals also agreed at a meeting of senior officials at the border village of Panmunjom to establish a liaison office at the North Korean border town of Kaesong and hold sports talks on fielding combined teams for 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 as part of efforts to plan the summit, which may take place June 12 in Singapore.
South Korea's Unification Ministry said the Koreas agreed to set up the liaison office at a factory park in Kaesong that had been jointly operated by the countries until the South shut it down in February 2016 after a North Korean nuclear test. The Koreas agreed to hold the military talks at Panmunjom on June 14 and the Red Cross talks on June 22 at the North's Diamond Mountain resort.
The talks between sports officials were set for June 18 at Panmunjom, the ministry said.
"If we continue to engage with each other like we did today, there will be no problem that can't be solved between the South and North," South Korean Unification Minister Cho Myoung-gyon said after the meeting.
Panmunjom has also been the site of pre-summit negotiations between American and North Korean officials. The American delegation is led by Sung Kim, the U.S. ambassador to Manila, who said on Friday that a summit between Washington and Pyongyang would provide an opportunity to "lead our two countries into new era of security, prosperity and peace."
South Korean President Moon Jae-in, who met with Kim Jong Un twice in the past two months, has said progress in inter-Korean reconciliation will be a crucial part of international efforts to resolve the nuclear standoff with North Korea because the North won't give up its nuclear program unless it feels its security is assured.
Ri Son Gwon, chairman of the North Korean agency that deals with inter-Korean affairs, told Cho at the start of the meeting that the rivals should work on building "trust and consideration for each other" to carry out the agreements forged at the recent inter-Korean summits.
When Moon and Kim met for their first summit at Panmunjom in April 27, they spoke of vague aspirations for a nuclear-free Korean Peninsula and permanent peace, which Seoul has tried to sell as a meaningful breakthrough that increases the chances of successful nuclear negotiations between Trump and Kim.
But relations chilled when North Korea canceled an inter-Korean meeting and threatened to walk away from the summit with Trump because of the South's participation in regular military exercises with the United States and comments from U.S. officials. Trump canceled the summit, then said it may still take place, shortly before Kim and Moon met again and agreed to resume high-level talks between their countries.
Talking to South Korean reporters ahead of Friday's meeting, Ri seemed irritated when asked whether North Korea sees its grievances as resolved, saying reporters must ask questions that "meet the demand of changing times." When asked about the potential Trump-Kim meeting, Ri replied: "Go fly to Singapore to ask that question. This is Panmunjom."