“We are aware of the reports and refer you to the Republic of Korea,” the statement said. “The United States remains open to credible talks on the denuclearization of the Korean Peninsula. However, conditions must change before there is any scope for talks to resume.”
The statement repeated the requirement that the North must abandon its nuclear and missile programs, which Mr. Kim has said he will never do because they are his guarantee against an American-led effort to topple North Korea’s government.
The South hoped to send a military delegation to the border village of Panmunjom on Friday to discuss “stopping all hostile activities that raise military tension” along the border, Vice Defense Minister Suh Choo-suk said on Monday.
Mr. Kim proposed such talks in a May 2016 speech. But Park Geun-hye, a conservative president of South Korea who has since been impeached and removed from office, rejected the offer, calling it insincere and demanding that the North first move toward dismantling its nuclear weapons program.
Mr. Moon reaffirmed his commitment to dialogue in a speech in Berlin this month, days after Pyongyang conducted its first test of an intercontinental ballistic missile.
The South’s outreach comes as the United States is reviewing its economic, military and covert options to deal with the North Korean threat.
After trying to persuade China to intervene more heavily, Mr. Trump has suggested that the United States will go its own way, and that effort seems quite likely to begin with new sanctions on small Chinese financial institutions that do business with North Korea. Chinese trade with the North has increased over the past year, even as Beijing has said it is complying with United Nations sanctions on specific transactions, including the importation of coal.
At the same time, the United States has bolstered its naval presence off the Korean Peninsula and continued cyberattacks aimed at slowing the North’s missile testing. But it is not clear whether that effort, which seemed to enjoy some success between 2014 and 2016, is still fruitful.
Mr. Suh, the South’s vice defense minister, proposed on Monday that the North restore a military hotline that Pyongyang cut off in 2016 amid tensions after its nuclear test in January of that year. Without the hotline, the two militaries have no means of communicating quickly and directly to avoid an unintended conflict.
South Korea did not disclose what it wanted to discuss if military talks were held. In past meetings, North Korea has demanded that the South stop holding joint military exercises with the United States and end the use of loudspeakers to broadcast propaganda along the border. South Korea has recently accused the North of sending military drones to spy on the South, an issue that Seoul would quite likely raise.
Also on Monday, the South Korean Red Cross Society proposed an Aug. 1 meeting at Panmunjom with its North Korean counterpart to arrange reunions of relatives in the North and South who have not seen each other since being separated in the 1950s during the Korean War.
Those reunions, which have been held occasionally over the years, are a highly emotional issue and are widely seen as a barometer of inter-Korean relations. Mr. Moon said in his Berlin speech that the reunions should resume.
The last such meetings were held in 2015, when fewer than 100 older Koreans from each side were allowed to spend three days with their family members. About 60,000 South Koreans are still hoping for a chance to see spouses, siblings and parents across the border before they die. More than half of them are in their 80s or older.
North Korea has said it will not allow another round of reunions unless the South sends 12 North Korean waitresses back to the country. South Korea has said that the women, who worked at a North Korean restaurant in China, chose to defect to the South with their manager last year, but Pyongyang accused the South of kidnapping them.
Pyongyang has also demanded the return of Kim Ryen-hi, a North Korean defector in the South who has said she made a mistake and wants to go back. South Korea has said there are no legal grounds for sending her back to the North.
The United Nations Security Council is discussing a new set of sanctions against North Korea over its intercontinental ballistic missile test. The North has warned that such a move would lead to unspecified retaliatory measures, which analysts said might include another nuclear or long-range missile test.
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