The North Korean soldier was spotted moving towards South Korea, and then crossed over a military demarcation line separating the two sides, the South's Joint Chiefs of Staff said in a statement.
South Korea's President Moon Jae-in is determined that this railway project will go ahead, says our correspondent.
Despite the warming ties, it remains unclear whether the North's leader Kim Jong Un will make his first-ever visit to the South this year, as Seoul is hoping.
Moon held a brief press meeting on his way to New Zealand from the the G-20 summit in Buenos Aires, Argentina.
"We're getting along very well".
A second Trump-Kim Jong Un meeting, originally expected to take place before the end of 2018, could now be less than two months away.
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Trump said, "I think we're going to do one fairly (soon) - you know, into January, February, I think", while travelling back from Argentina after G20 summit.
During the 18-day trip experts from both countries will travel more than 2600 km across almost all of North Korea. Ban said he hopes the summit will occur at a time when the worldwide community feels confident about North Korea's commitment to denuclearization.
South Korea sent rail cars and dozens of officials to North Korea on Friday for joint surveys on northern railway sections the countries hope someday to connect with the South.
"The crisis is still continuing because of North Korea's development of nuclear, missile and weapons program and materials", Ban said.
But differences remain between Washington and Seoul on how to proceed with Kim, as the dovish Moon favours more robust engagement with the North.
Before that, however, the president had mocked the communist ruler, calling him "Little Rocket Man", while Kim had in turn said Trump was a "mentally deranged USA dotard", a word that suggests senility.