The North Korean leader, Kim Jong-un, had proposed such talks in a May 2016 speech. But the South’s then-president, Park Geun-hye, a conservative 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.
Mr. Suh, the vice defense minister, on Monday called on the North to restore a military hotline that Pyongyang cut off in 2016, amid tensions following 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 specifically 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 be likely to raise.
Also Monday, the South Korean Red Cross Society proposed a meeting at Panmunjom on Aug. 1 with its North Korean counterpart, to arrange reunions of relatives in the North and South who have not seen each other since being separated during the 1950-53 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 elderly 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 wives, 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…