The Red Cross has also proposed a meeting to try to revive the meetings between Korean families separated since the War (1950-1953).
South Korea's new government is making overtures to the North, proposing military talks at the Demilitarized Zone (DMZ) that separates the two rivals.
The reunions are a highly emotional issue because most applicants are in their 70s or 80s and are desperate to see their loved ones before they die.
North Korea will likely accept Moon's proposed talks on easing border animosities, as it's something that it's previously called for.
If held, it would be the first such meeting between military authorities of the two sides since a working-level meeting that failed to produce an agreement on October 15, 2014, at Panmunjom, according to Yonhap News Agency.
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News of the revision comes as Republicans delay their summer recess by two weeks to mid-August, the news service writes . The Senate GOP is facing a slim margin for passage, with a couple of lawmakers already saying they won't approve it.
Kang Mi-jin, a defector who speaks regularly to market sources inside North Korea and reports commodity prices for Daily NK, said the price spikes in recent weeks were caused initially by the rumours - later confirmed - that China was restricting the flow of oil to North Korea.
South Korea's Defense Ministry made the offer on Monday morning, the first since Moon Jae-in became the South's president. "The proposal to restart reunions of separated families is a follow up to President Moon Jae-in's Berlin Declaration, which attempts to ease tensions on the Korean peninsula and open up a channel of dialogue with Pyongyang".
South Korea's policy is consistently centered on making the Korean Peninsula free from the threats of nuclear weapons and war, he said. After the North fired an ICBM on July 4, Moon quickly condemned the launch as a "reckless" and "irresponsible" provocation. In 2015, her government deported a South Korean-born American citizen who had spoken warmly about her trips to North Korea in public appearances and articles in South Korea.
But Pyongyang has staged a series of missile launches in violation of United Nations resolutions - most recently on July 4 when it test-fired its first ICBM, a move which triggered global alarm and a push by US President Donald Trump to impose harsher United Nations sanctions. Pyongyang has yet to respond.
Seoul's olive branch comes as US President Donald J. Trump signals frustration with the pace of efforts by China, North Korea's long-time ally and top trading partner, to pressure Kim back to the bargaining table.
The military demarcation line is the border that bisects the two Koreas. Also, there have been many cases of abductions of South Koreans, in addition to Pyongyang's reckless nuclear weapons programme. It is anxious about an influx of refugees and possible USA troops stationed on its border in a unified Korea.