Trump also said that "at some point" he would invite Kim to visit the US, though he gave no indication of when.
South Korean officials planned to debrief him to try to determine his motive for defecting, the military said.
U.S. President Donald Trump says his next summit with North Korean leader Kim Jong-un will likely take place in January or February, and, he says. there are three venues under consideration.
It marked the first time in a decade that a train from the South entered North Korea. However, a North Korean soldier has now achieved this feat.
Prospects for a second summit to overcome a current logjam in negotiations will likely depend on whether either the US or DPRK can show flexibility with regards to offering gestures surrounding sanctions relief or steps towards denuclearization.
North Korean and South Korean soldiers are pictured during an operation to reconnect a road across the Military Demarcation Line inside the Demilitarised Zone (DMZ) separating the two Koreas (Novemeber 22, 2018).
The South Koreans and their counterparts will live in the train, inspecting two railway lines for a total of 18 days - one linking the North's southernmost Kaesong City to Sinuiju City near the Chinese border, and the other connecting Mount Kumgang near the inter-Korean border to Tumen River bordering Russian Federation in the east.More news: Girl's Letter to Steph Curry Changed How Under Armour Sells His Shoes
"You will visit train stations and cross hills and rivers in North Korea no outsiders have visited", Unification Minister Cho Myoung-gyon told the survey team, according to the Washington Post.
More than 30,000 North Korean civilians have fled their homeland but most flee across the porous frontier with China, and rarely across the inter-Korean border which is fortified with minefields and barbed wire. The postponement stirred concerns that nuclear talks between the USA and North Korea had again bogged down, as Kim's regime seeks sanctions relief before taking key disarmament steps. First, the specialists will survey the central to northwestern rail.
The US has urged North Korea to take concrete steps towards denuclearization, whereas Pyongyang has demanded guarantees for its survival before the signing of a peace treaty.
But differences have emerged between Washington and Seoul on how to proceed with Kim, as the dovish Moon has long favored engagement with the North.
The North Korean leader said he would visit Seoul "in the near future", during his third summit with Moon in September.
The two leaders said Kim's visit to the South Korean capital "would provide additional momentum to their joint efforts to establish peace on the Korean peninsula", Moon's press secretary Yoon Young-chan said.