During a January 4 phone call in which the South Korean leader briefed the American president on the plans for talks with North Korea, Trump asked Moon to publicly give him the credit for creating the environment for the talks, according to people familiar with the conversation.
Later that night, Trump tweeted that the talks wouldn't be happening "if I wasn't firm, strong and willing to commit our total 'might' against the North". At a news conference six days later, Moon agreed that Trump deserved "huge credit" for the talks.
Moon is trying to manipulate Trump into effectively undermining his own policy: putting pressure on North Korea, said one former official.
"Kim Jong Un is setting the agenda here," the person said. "His purpose is to use these talks to show the world that he's okay and to make the sanctions effort lose steam."
Since taking office last May, Moon has repeatedly made overtures to North Korea but Kim consistently rebuffed them all — until New Year's Day, that is. Then, just weeks after declaring that his nuclear weapons programme was complete, the North Korean leader called for "detente" with the South.
This prompted a flurry of activity in the South, including getting Trump to agree in that January 4 phone call to postpone joint military drills until after the Olympics, to avoid antagonising North Korea.
Further evidence of Kim's agenda-setting: The first item for discussion last week involved the performances of a North Korean propaganda orchestra known for numbers such as Our Comrade Kim Jong Un.
Then came the inclusion of a 240-member cheering squad known as an "army of beauties" because these squads have previously been made up entirely of attractive young women — and have been immensely popular in the South.
Seoul also agreed to combine the two Koreas' women's ice hockey teams — against the strong objections of the Southern team — and agreed to send Southern skiers to train on far inferior slopes in the North over the next few weeks.
The concessions to North Korea have angered many South Koreans, with some publicly wondering whether they're the Pyeongchang or the Pyongyang games. More than 31,000 people have signed an online petition calling on the president's office not to combine the hockey teams. "Politics should not be involved in sports.
Is this a fair process, a just result?" wrote one signer. A Realmeter poll found half of respondents thought the two Koreas should march separately under their own flags, while 40 per cent supported the agreement that they should march together under a flag showing a unified Korean Peninsula.
High-ranking officials will visit South Korea as part of the Olympic delegation — including perhaps North Korea's de facto No. 2, Choe Ryong Hae. If he comes to Seoul, which would require his being removed from South Korea's sanctions list, Moon would hope to meet him, according to aides.
The Moon Administration is trying to build trust with the North in the hope this will lead to talks about its nuclear weapons programme — although Kim's regime has made it clear that this is not an inter-Korean issue.
That process has gained extra urgency as Trump and his aides have talked increasingly about using military options to teach North Korea the error of its ways.
"When our Government has talked to the Trump Administration, we have always emphasised that the Olympics can be an excuse for North Korea to come out for talks," said Kim Hong Gul, the son of former South Korean President Kim Dae Jung, who won the Nobel Peace Prize for meeting Kim Jong Il in 2000.
Kim Hong Gul met the current North Korean leader at Kim Jong Il's funeral in 2011 and is now an influential voice on inter-Korean relations in the ruling Democratic Party. "Our Government has even more reason than ever to talk to North Korea because the stakes are now so much higher. We need to make sure war doesn't break out."
That could also be the reason for Kim Jong Un's change of heart, said Cheong Seong Chang, an expert on North Korea's leadership at the Sejong Institute. "Kim Jong Un bragged about the nuclear button on his desk but he can't rule out the chance that the US will resort to military options, so he might be trying to buy some time."
But it could also be because international sanctions are starting to hurt.
Regular visitors to North Korea say that China has cracked down on border trade to a surprising extent, conducting thorough inspect-ions of all goods going into and coming out of North Korea.
There are plenty of ways Moon's efforts could go off the rails. Immediately after the Olympics, South Korea and the US are set to begin their postponed military drills, which in recent years have included practicing decapitation strikes on North Korea's leadership.
Chun Yung Woo, a hawkish national security adviser, said that this short-term reprieve could lead to longer term problems. "Once all the diplomatic options have been exhausted. Moon will have even fewer options left for dealing with North Korea."
That, analysts say, could embolden Trump aides like National Security Adviser H.R. McMaster, who argues that time for dealing with North Korea is running out. And it will be much harder then for Moon to flatter Trump into thinking otherwise.
