The White House said Moon had briefed Trump on the outcomes of the North-South talks on Tuesday, and "thanked President Trumpfor his influential leadership in making the talks possible".
North Korea has become Trump's most urgent foreign crisis, as he struggles to contain the regime's rapidly advancing nuclear weapons and ballistic missile programs.
He said in a news conference later that the USA had problems with Pyongyang, but a lot of good talks were going on. Trump has denied pursuing a "bloody nose" strategy and agreed with South Korea to delay an annual joint military exercise that was scheduled to take place during the Winter Olympics.
It added that the two leaders hoped the latest dialogue effort would lead to a peaceful resolution of the North Korean nuclear issue and the establishment of peace on the Korean Peninsula, beyond next month's Olympics.
Impeached South Korean president Park Geun Hye shut down operations at Kaesong in February 2016 in retaliation for a North Korean satellite launch.
South Korean President Moon Jae-in said Wednesday that US President Donald Trump "deserves big credit" for his country's talks with NKorea.
Kim and US President Donald Trump have exchanged fiery barbs in the past year and Trump has warned that the United States would have no choice but to "totally destroy" North Korea if forced to defend itself or its allies.
No sitting U.S. president, according to Gordon Chang, an author and expert on North Korea, has ever talked to the current Kim family ruler in North Korea.
Also, a military hotline between the two countries was opened.
The high-level talks were held at the border village of Panmunjom, where the South Korean cabinet minister in charge of relations with the North, Cho Myoung-gyon, and his North Korean counterpart, Ri Son-kwon, deliberated for 11 hours.
Conservatives often support a more aggressive foreign policy because it leads to deterrence - scaring rogue actors like North Korea into deciding not to attack others and spark wars.
In October, Mr. Trump said in a tweet that he told Secretary of State Rex Tillerson was "wasting his time trying to negotiate with Little Rocket Man" - a reference to North Korea's leader.
A senior South Korean government official noted that the North Korean regime will have no choice but to hold talks with the USA if it wanted to develop its stagnating economy.