The last defection involving North Koreans occurred in May when two civilians aboard a small boat fled to the South across the Yellow Sea.
When asked on Saturday if he would ever host Kim in the United States, the Republican president replied: "At some point, yeah".
There is a passenger coach, a sleeping coach, an office coach and a wagon loaded with water for showers and laundry.
During the surveys, a North Korean train engine will pull six South Korean rail cars - including passenger and sleeping cars, a power-generator vehicle and a fuel tanker - along the North Korean tracks to test operability.
Cho Myoung-gyon, who heads the Unification Ministry which oversees relations with North Korea, said the project was "intended to overcome division and open a new future of the Korean Peninsula".
Seoul said the survey was purely aimed at gathering information on the current state of the North's rail system and assured that actual restoration works would come only after consents from the UN.
"Through the one connected railway, the South and the North will prosper together and the ground for peace on the Korean Peninsula will be consolidated".More news: Murder charge for Botham Jean's killer
More news: Packers fire McCarthy following loss to Cardinals
More news: Meghan Markle Reads Poem at Christmas Carol Concert With Prince Harry
A U.S. thinktank said in November it had identified at least 13 of an estimated 20 active undeclared missile bases inside North Korea, underscoring the challenge for American negotiators hoping to persuade Kim to give up his weapons programmes.
The joint railway surveys were on hold before the U.N. Security Council on Saturday granted an exemption to sanctions that allowed them to proceed.
The two Koreas have made significant progress in improving their relationship over the past year.
And days before the meeting between Xi and Trump in Buenos Aires, an adviser to China's foreign ministry said it would be "impossible" for North Korea to completely give up its nuclear weapons, and the USA should instead focus on more incremental progress.
The study comes as differences emerge between Seoul and Washington, which stations 28,500 troops in the South as part of their decades-old alliance.
After their third meeting in Pyongyang, North Korea's capital, in September, Moon said Kim agreed to make a reciprocal visit to Seoul this year.