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North Koreans take the hands of their departing South Korean family members (on bus) as they bid farewell following their three-day family reunion of people separated by the Korean War in the 1950s, at the North Korean Mount Kumgang resort, Sept. 28, 2009. The most recent of these government-arranged reunions was in February 2014. Getty Images

South Korea said it sent a proposal Friday to North Korea suggesting the rival nations meet Sept. 7 to discuss holding family reunions for relatives separated by the Korean War of 1950-1953, Yonhap reported. Seoul's Red Cross suggested representatives meet at its Peace House inside the Demilitarized Zone, where the two countries recently held talks resulting in the decision to de-escalate tension in the area. One of the agreements in their deal was to explore holding the reunions.

South Korean Red Cross President Kim Sung-joo reportedly sent a message to Pyongyang Red Cross President Kang Su-rin requesting the Sept. 7 talks at about 9:50 a.m. "It's important to note the government nowadays oversees the work of the Korean Red Cross over issues about separated families, and any related progress can only be made with our approval," an anonymous official with the Ministry of Unification told the Korea Times. "The Korean Red Cross consulted us before sending its message to the North on Friday."

Thousands of families were separated in the Korean War of the 1950s, and about 66,000 affected South Koreans were estimated to still be alive, most of them over age 80. The two governments have held nearly 20 family reunions, where they allow groups of relatives to briefly meet at locations like the Mount Kumgang resort in North Korea, since 1985. The last reunion was in February 2014 and had 2,200 South Korean participants. South Koreans are usually prevented from entering North Korea.

Seoul has proposed scheduling reunions around the time of Chuseok, an annual fall harvest festival known as Korea's Thanksgiving Day. This year, Chuseok falls on Sept. 27.

The impetus for the proposal came during the peace talks held earlier this week. South Korea agreed to stop its propaganda broadcasts at the border after the North reportedly expressed regret over a land mine blast that injured two of Seoul's soldiers. They kept their options open and announced they'd meet again soon, International Business Times previously reported.

"For us, the family reunion issue tops the agenda," a South Korean spokesman told Deutsche Presse-Agentur International. "If the North wants to show us they are taking the agreement seriously, they can do so by solving this issue first."