The North Korean military stated that even though the 8th US Army Command on Tuesday moved to a new base in Pyeongtaek, some 70 kilometers (43 miles) south of Seoul, the North can still successfully target the facility.
The South also proposed separate talks by the rival states' Red Cross organisations to resume a humanitarian project to reunite families separated during the 1950-53 Korean War in closely supervised events held over a few days.
"We make the proposal for a meeting. aimed at stopping all hostile activities that escalate military tension along the land border" that is also the Military Demarcation Line between the long-hostile neighbors, the ministry announced in a statement.
The Oct. 4 declaration was the outcome of the inter-Korean summit that was held in Pyongyang in 2007 between late South Korean President Roh Moo-hyun and late DPRK leader Kim Jong Il, father of the current leader Kim Jong Un.
The last government-level talks were held in December 2015.
Seoul's Red Cross says it wants separate talks at the border village on August 1 to discuss family reunions, with possible reunions over the Chuseok holiday, which falls in October this year.
The offer comes after the North claimed to have conducted the first test of an intercontinental ballistic missile (ICBM) earlier this month, and said it had mastered the technology to mount a nuclear warhead on the missile.More news: Ed Sheeran's Appearance Of 'Game Of Thrones'
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"Because we have reached the tipping point of the vicious cycle of military escalation, and thus, the need for dialogue is more pressing than ever before", he said.
North Korea has conducted two nuclear tests since the beginning of previous year and missile-related activities at an unprecedented pace.
In response to Liberty Korea Party lawmaker Yoon Sang-hyun's question on plans for sanctions against North Korea, Kang responded that the government was "currently negotiating a secondary [boycott] option with the U.S.".
This photo, taken on July 6, 2017, shows South Korean President Moon Jae-in delivering a speech in Berlin over his vision for bringing peace to the Korean Peninsula.
In the proposal for talks, South Korea did not elaborate on the meaning of hostile military activities, which varies between the two Koreas. Typically, Pyongyang would like to end the routine joint military drills undertaken by South Korea and the United States along the border, while Seoul would like the loudspeaker propaganda broadcasted by both sides to cease. Two quakes measuring 5.1 and 5.8 jolted southeastern South Korea on September 12, causing no casualties.
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. Moon's conservative predecessor, Park Geun-hye, had refused to engage in substantive dialogue with Pyongyang unless the isolated regime made a tangible commitment to denuclearisation.
"If the South and the North sit down face to face, matters of mutual interest could be discussed in a candid manner", Cho told reporters.