The two countries will also form a unified women's hockey team to compete in the Winter Olympics in February. The North will send a cheering squad to support its delegation.
The president said any talks with North Korea would have to be "under the right circumstances." He spoke to South Korea's leader on Wednesday, after the two Koreas held high-level talks.
The two sides announced further dialogue to ease tension between them, but the North still insists any talk of nuclear weapons is off the table.
North Korea is known for its extensive military tunneling. Along with training thousands more troops, officials say the Pentagon is buying specialized gear such as night vision goggles.
It was the first such talks between the two countries in two years, with Seoul hoping for further dialogue that might lead to reunions between families divided by decades-old standoff.
South Korea says they will discuss North Korea's participation in February's Olympics. It's a sign of easing tensions after the North Korean leader announced he has a nuclear button on his desk.
After trading bellicose barbs with North Korea throughout 2017, the U.S. heads into 2018 with an increasingly capable foe and no clear diplomatic exit ramps to temper the tensions.
One suspected transfer was seen in U.S. reconnaissance photos; South Korean media say ships have sold oil to North Korean vessels about 30 times since October.
"The fire engulfed an eight-story building and trapped dozens inside," NPR's Elise Hu reports from Seoul. "At least 15 of the dead were trapped in a second floor sauna."