North Korea has yet to respond to the latest overture.
He said such dialogue was crucial for those who seek the end of Pyongyang's nuclear weapons programme.
South Korean Unification Minister Cho Myoung-Gyon also called for the restoration of military and government hotlines across the border, which had been cut by the North a year ago in response to the South imposing economic sanctions after a nuclear test by Pyongyang, Reuters reported on July 16.
He urged all countries to implement United Nations sanctions and called on China and Russian Federation to use their influence to play "an even more constructive role" with North Korea.
"I think the President has made clear in the past with respect that any type of conditions that would have to be met are clearly far away from where we are now", White House spokesman Sean Spicer told a news briefing.
Seoul wants to have the meeting at Tongilgak, a North Korean building in the truce village of Panmunjom, the South Korean Ministry of National Defence said on Monday (17 July).
If the government meeting goes ahead, it will mark the first official inter-Korea talks since December 2015.
South Korea Wants Talks Not Hostility With North
Moon has said he would use both dialogues and pressures to resolve the standoff over North Korea's nuclear program. The Trump administration has yet to see what it considers a sufficient response from China.
South Korea on Monday offered talks with North Korea to ease animosities along their tense border and resume reunions of families separated by their war in the 1950s.
China, which has close ties to Pyongyang despite its anger over North Korea's missile and nuclear tests, welcomed the proposal, saying cooperation and reconciliation could help ease tensions.
But analysts say North Korea may accept the defense talks because it wants the South Korean army to halt loudspeaker broadcasts at the border that began after North Korea's fourth nuclear test in January 2016.
It is the first formal offer of military talks since South Korean President Moon Jae-in came to power in May, who pledged to reduce friction and engage with Pyongyang during his successful election campaign.
Treasury Secretary Steven Mnuchin said at the time that the measures were "in no way targeting China" but instead focused on "North Korea's external enablers".
"The fact that we wish to take on a leading role in resolving this (North Korean) issue has already been understood at the summit with the United States and the Group of 20 summit meetings", Cho said on Monday. He had proposed dialogue and other modes of engagement with Pyongyang, including extending an invitation to North Korean delegates to the 2018 Winter Olympics that the South will be hosting in its Pyeongchang county.
Pyongyang cut off direct communications with the South in February 2016, leaving Seoul no other choice but to convey their message openly through the media, government sources said.
Previously, Pyongyang has repeatedly said it refuses to engage in all talks with the South unless Seoul turns over 12 waitresses who defected to the South a year ago.