North Korea's multiple missile tests in recent months, culminating with its first-ever successful launch last week of an intercontinental ballistic missile capable of reaching Alaska, has alarmed the worldwide community and presented Trump's first major foreign policy test.
Tongilgak is a North Korean building at the Panmunjom truce village on the border used for previous inter-Korea talks.
Trump has complained that trade increased between the two despite calling on his Chinese counterpart Xi Jinping to use the nation's unique diplomatic and economic clout over North Korea as leverage.
If the government meeting goes ahead, it will mark the first official inter-Korea talks since December 2015.
The South Korean Red Cross on Monday proposed talks with the North to discuss reunions of family members separated during the Korean War. The aim would be to end "all acts of hostility" around the inter-Korean Military Demarcation Line, according to a Defense Ministry statement cited by the Yonhap News Agency.
The Oct. 4 declaration was the outcome of the inter-Korean summit that was held in Pyongyang in 2007 between then South Korean President Roh Moo-hyun and then DPRK leader Kim Jong Il, father of the current leader Kim Jong Un.
The vice defence minister did not elaborate on the meaning of hostile military activities, which varies between the two Koreas.
Primary users of fuel products in North Korea include fishermen, farmers, truckers and the military.
The sanctions are meant to apply meaningful pressure on a government which is all but single-handedly propping up a regime that threatens South Korea, Japan, and the United States with nuclear destruction.
Moon suggested earlier this month hostile military activities at the border be ended on July 27, the anniversary of the 1953 armistice agreement that ended the Korean War.
Tensions rose after North Korea's test this month of an intercontinental ballistic missile that could reach the U.S. mainland.
Frustrated that China has not done more to rein in North Korea, the Trump administration could impose new sanctions on small Chinese banks and other firms doing business with Pyongyang within weeks, two senior USA officials said.