If they were genuinely grateful to Mr. Trump, they were also seen as stoking the ego of the impulsive American leader so that he would continue to support South Korea’s efforts to resolve the North Korean crisis through dialogue.
On Monday, Mr. Trump mentioned in a tweet the possibility of meeting Mr. Kim at the border between North and South Korea, where Friday’s meeting between Mr. Kim and Mr. Moon was held.
Mr. Trump has also been eager to take credit for Mr. Kim’s shift in behavior as the inter-Korean summit has fanned speculation that he could receive the Nobel Peace Prize.
“That’s very nice, thank you. That’s very nice,” a visibly flattered Mr. Trump said in response. “I just want to get the job done.”
Senator Lindsey Graham, a Trump ally who is sometimes critical of the president, said that if Mr. Trump “can lead us to ending the Korean War” while “getting North Korea to give up their nuclear program” in a verifiable way, then he “deserves the Nobel Peace Prize and then some.”
But some were skeptical about Mr. Trump’s chances — including his own son. “The globalist elite would never give him that win,” Donald Trump Jr. tweeted on Friday.
No matter what the likelihood is for Mr. Trump’s getting a Nobel, his public image among South Koreans has been improving markedly as the mood on the Korean Peninsula shifts from fears of war to hopes of peace.
During their summit meeting, Mr. Kim and Mr. Moon agreed to push for talks with Washington to negotiate a peace treaty to formally end the 1950-53 Korean War, an agreement that, to the pleasant surprise of many South Koreans, a usually tempestuous Mr. Trump has eagerly endorsed.
Last year, as tensions escalated on the Korean Peninsula, with Mr. Trump’s administration openly threatening military action against North Korea, Mr. Moon publicly denounced such talk, swearing that no such military action would take place without South Korea’s consent. When Mr. Trump visited Seoul in November, weeks after he threatened to “totally destroy” North Korea, protesters took to the streets in Seoul, calling him “a war maniac.”
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These days, it is easy to find citizens and political analysts in South Korea who mouth something few would have imagined a few months ago: support for giving Mr. Trump, Mr. Kim and Mr. Moon the Nobel Prize together should they achieve lasting peace.
Such talk reflects rising hopes for coming discussions between Mr. Trump and Mr. Kim, the first summit meeting between the leaders of the United States and North Korea, which could happen by early June.
Skeptics, however, say that Mr. Kim might be duping Mr. Moon and Mr. Trump into a false peace.
To whet Mr. Kim’s appetite for a deal, Mr. Moon on Friday handed Mr. Kim a computer thumb drive that contained detailed plans to rebuild the North’s decrepit economy if Mr. Kim denuclearizes his country, aides to Mr. Moon said.
And when Mr. Kim talked alone with Mr. Moon, without aides, he sought Mr. Moon’s advice for his coming talks with Mr. Trump, they said. Mr. Moon found Mr. Kim forthright and courteous, they said.
Still, the prospect that Mr. Kim could even be considered for a Nobel is likely to alarm human rights activists. He has been accused of ruthlessly executing scores of aging generals and party elite members, including his own uncle. Mr. Kim has also been accused of masterminding the fatal poisoning of his half brother.