On Monday, Seoul's Defense Ministry proposed talks at the border village of Panmunjom this Friday to discuss how to ease border-area tensions, while the Red Cross said it wants separate talks at Panmunjom on August 1 to discuss family reunions.
The South Korean government separately proposed reopening Red Cross talks to discuss ways to resume family reunions.
The talks are expected to be held on Friday (21 July) and come as the latest attempt by Seoul to suspend "hostile activities" at their joint border and after a series of missile tests, including the recent launch of an intercontinental ballistic missile (ICBM) by North Korea. The reunions are widely seen as a barometer of inter-Korean relations.
North Korea gets most of its fuel from China, with some coming from Russian Federation.
The last time the arch-rivals held military-level talks to ease tensions was in 2014 but they failed to reach an agreement then. However, past history has shown that North Korea's leader, Kim Jong-un, is good at fooling the global community with displays of fake goodwill - which risk Washington and Seoul relaxing their vigilance.
After the North announced the successful launch of an intercontinental ballistic missile on July 4, Harris said it is getting "closer to being able to deliver a nuclear-equipped missile" to the USA mainland.
South Korea's President Moon Jae-in has long signaled he wants closer engagement with the North. A previous joint event was held in October 2015 to arrange the reunion of families separated by the 1950-1953 Korean War. "[The government] is looking forward to a positive response from the North Korean side".
In Asia-Pacific countries, many are concerned about North Korea's nuclear program
It has been reported that the U.S. has proposed a new draft UNSC resolution for further sanctions on North Korea to China. North Korea's biggest need is to pay for fuel, since the country doesn't come close to producing enough oil.
"After North Korea's frequent missile tests including its very first ICBM test, the global community has vowed to tighten sanctions and China simply can not exclude itself from the recent movement, although it probably does not want to indefinitely cut off fuel sales to the North", Mr Kang said.
The South Korean official added that the meeting aims to stop "all acts of hostility" near the Military Demarcation Line (MDL) that divides the two nations on the Korean Peninsula.
The North's latest ICBM launch has stoked security worries as it showed the country could eventually ideal a reliable nuclear missile capable of reaching anywhere in the United States.
Seoul's Unification Ministry says these latest proposals are in line with President Moon Jae-in's dual track policy to pursue both engagement with the Kim Jong Un government while also supporting USA led sanctions to pressure Pyongyang to halt its nuclear and ballistic missiles programs. He said now was North Korea's last best chance to change direction. Such dialogue was crucial for those who seek the end of Pyongyang's nuclear weapons program.
"We hope that the two Koreas will make efforts to break the stalemate and create conditions for a resumption of negotiations", foreign ministry spokesman Lu Kang was quoted as saying at a press briefing.
The ministry did not explicitly specify what "all hostile activities" includes, and the definition varies between the two Koreas.