"We should keep on watching North Korea's response in the future, but we will persistently endeavor to make these proposals realized without fluctuating between joy and grief according to [the North's] response", Cho told media.
It was unclear how North Korea will react since it remains suspicious of new South Korean President Moon Jae-in's outreach to it.
The North has conducted two nuclear tests since the beginning of a year ago and missile-related activities at an unprecedented pace. About 28,500 American troops are stationed in South Korea.
"The North Korean government maintains strict controls over their workers' profits, in some cases probably taking 90 percent of their wages", Scott Synder, the director of the Program on U.S. -Korea Policy at the Council of Foreign Relations, told Fox News.
The dialogue was aimed at stopping all hostile acts that escalate military tensions near the military demarcation line (MDL) dividing the two Koreas, the vice minister said in a statement.
China stopped importing North Korean coal but total trade has risen, which prompted Trump to complain last week Beijing is failing to use its economic leverage to stop Pyongyang's pursuit of nuclear weapons. Official talks between the sides have not been held since December 2015. In all, the North has conducted five nuclear tests and numerous missile tests.
Those talks would be held on August 1, also in Panmunjom - that is, if Pyongyang accepts.
If a meeting takes place, it will mark the first military talks between the neighbours in three years.
The last such reunions were held in October 2015 during the government of Moon's predecessor under a futile push for reconciliation following a sharp increase in tension over border incidents involving a landmine blast and artillery fire.
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While Cho says there is no "separation" between the US and South Korea on dealing with the North Korean nuclear threat, Washington continues to emphasize pressure over dialogue and is preparing new sanctions on Chinese banks and firms doing business with Pyongyang possibly within weeks, according to USA officials.
Beijing agreed in March 2016 to enforce United Nations sanctions following North Korea's test of a missile possibly capable of carrying a nuclear warhead.
The vice defence minister did not elaborate on the meaning of hostile military activities, which varies between the two Koreas.
"The U.S. conventional and nuclear forces, as well as South Korea and Japan's forces, greatly outstrip North Korea in terms of technology", Hanham asserted.
North Korea's ICBM is likely a deterrent, nothing more, as actually firing one off would be suicidal. Since no truce was agreed, the two sides remain technically at war.
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 has sent a proposal to North Korea for talks on easing military tensions and the reunion of separated families, Seoul's Ministry of National Defense (MND) and the Red Cross said on Monday.
North Korea says the South abducted the 12 waitresses and the restaurant manager and has demanded their return, but the South has said the group made a decision to defect of its own free will. Cho said this matter is not included on the talks agenda.