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".
For the first time since the recent elimination of border guards on the divided peninsula, a North Korean soldier has fled to the south.
South Korean authorities plan to question the defector over the details of his escape.
The six-carriage train is transporting 28 South Koreans including railway engineers and other personnel, and carrying 55 tonnes of fuel and an electricity generator.
Through Dec. 5, the South Koreans will team up with North Korean officials and experts to look at 400 kilometers of tracks along the western coast from Kaesong, just north of the inter-Korean border, all the way up to Sinuiju, near the border separating North Korea and China.
In November 2017, a North Korean soldier dashed through a hail of bullets fired by his fellow troops to enter the South through Panmunjom, the so-called truce village that straddles the border.
"We're getting along very well". He also said his administration is ready to lift the sanctions on North Korea, but asserted that Pyongyang has to be "responsive" to Washington.
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"This signals the start of co-prosperity of the North and the South by reconnecting railways", Transport Minister Kim Hyun-mee said.
But skepticism over the second Trump-Kim summit appears to be have cleared, as Trump told Moon that he wants to follow up on his historic June summit in Singapore.
US officials are seeking a "substantive next step" toward denuclearization, Secretary of State Mike Pompeo told CNN on Saturday, adding that Washington has been seeing good progress in discussions with Pyongyang.
"Given South Africa's experience of voluntarily abandoning its nuclear program for the sake of regional security, its denuclearization process can be a good model for North Korea", Moon was quoted as saying by spokesperson Yoon.
They have also begun work to reconnect a train line and fix another rail link across the border.
Kim agreed to travel to Seoul after hosting his South Korean counterpart Moon Jae-in in Pyongyang in September for their third summit but prospects of a fourth Moon-Kim meeting have recently dimmed, with negotiations on denuclearizing the North grinding to a halt.
Seoul plans to hold a groundbreaking ceremony before the end of the year on a plan to establish road and rail links between the two Koreas, first agreed upon by the countries' two leaders at a summit in April.