Moon reportedly thanked Trump for his "influential leadership in making the talks possible" and both leaders expressed support for Trump's "maximum pressure" campaign against North Korea, which has seen heightened military threats and a chain of nuclear threats flying both ways across the Pacific.
The commentary says that the US-South Korea exercises and inter-Korean dialogue are incompatible and that the drills should be completely stopped rather than postponed. The deal marks the first time that athletes from the North will compete in a South Korean Olympics, as North Korea boycotted the 1988 Olympics in Seoul.
But the president made little mention of what else came of the talks - perhaps because, as many in the South and overseas noted, it was Pyongyang that maintained the upper hand.
An agreement on the North's Olympic participation had been widely expected before the talks, but the Koreas appeared to remain sharply at odds over how to improve their overall ties. The meeting may have given the impression that tensions between Seoul and Pyongyang are easing, at least temporarily, but no progress was made on the issue of North Korea's development of nuclear weapons and ballistic missiles - the biggest source of regional tension.
"Who knows where it leads?" he said.
The Russian president insisted the only way to resolve tensions in Korean peninsula region is through dialogue. Technically, South Korea and the United States remain at war with North Korea after the Korean War ended in 1953 with an armistice instead of a peace treaty.
Moon invited his Chinese counterpart to the closing ceremony of the PyeongChang Winter Olympic Games, which will be held February 9-25.
Some in the South are concerned as well.
Trump has been of late more open, on more than one occasion, to having a dialogue with North Korea.
The dominant Korean Workers' Party, judicial authorities, and administrative officials are organizing members for their joint non-socialist elements team, he said.
North Korea disagreed with Moon's assessment.
Trump also said he wants to maintain pressure on North Korea, urging China and other countries to withhold economic aid to Kim Jong Un until he gives up his nuclear weapons programs.
The vessel is under South Korean sanctions implemented during the previous Park Geun-hye administration.
Scott Snyder: I believe that South Korea has also historically been concerned about Japanese capabilities. Resuming joint operations with the North at the Kaesong industrial complex or trips to the Mount Kumgang tourist area would thus be considered only in the context of United Nations sanctions, Moon said. Tuesday's historic talks only showed how hard that will be.