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SINGAPORE, SINGAPORE - JUNE 12:  In this handout photograph provided by The Strait Times, North Korean leader Kim Jong-un (L) with U.S. President Donald Trump (R) during their historic U.S.-DPRK summit at the Capella Hotel on Sentosa island on June 12, 2018 in Singapore. U.S. President Trump and North Korean leader Kim Jong-un held the historic meeting between leaders of both countries on Tuesday morning in Singapore, carrying hopes to end decades of hostility and the threat of North Korea
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Trump touts confidence in Kim Jong Un
(CNN) —  

President Donald Trump continued to defend his budding relationship with North Korean leader Kim Jong Un on Monday, demanding credit for his role in making “initial steps toward a deal” by establishing a personal rapport with the young dictator during last week’s summit in Singapore.

“If President Obama (who got nowhere with North Korea and would have had to go to war with many millions of people being killed) had gotten along with North Korea and made the initial steps toward a deal that I have, the Fake News would have named him a national hero!” Trump tweeted.

Amid lingering skepticism over North Korea’s commitment to complete denuclearization in the wake of the Singapore summit, Trump has aggressively pushed the idea that Kim is sincere in his intentions and that the two leaders were able to develop a unique chemistry.

It’s a conviction South Korean officials share. South Korean Vice Foreign Minister Lim Sung-Nam said Monday in Washington that any diplomatic progress should be credited to the connection that Trump and Kim established through an “unprecedented top-down approach” to negotiations.

“The actors for this top-level diplomacy are completely different leaders as compared to the past,” Lim told an audience at the Center for Strategic and International Studies. “Moreover, the personal chemistry between them has been unique as well.”

Trump trying to butter-up Kim?

South Carolina Republican Sen. Lindsey Graham, asked about Trump’s praise for Kim, suggested the President is as willing to use carrots as he would be – if necessary – to use sticks. “If you try to play Trump or back out, there’s going to be a war and nobody wants war,” Graham told CNN.

Trump’s claims to a cozy relationship may reflect an effort to butter-up Kim “to make it easier to get a better deal,” Florida Republican Sen. Marco Rubio told CNN last week.

Indeed, the administration hopes that Secretary of State Mike Pompeo can build on that rapport to create substantial movement toward denuclearization.

But sources have told CNN that there is nothing to suggest that North Korea has begun destroying its missile launch sites, despite Trump’s repeated claims to the contrary and his declaration last week that the country is no longer a nuclear threat.

Harry Harris, Trump’s nominee to be ambassador to South Korea, said last week that North Korea continues to be a nuclear threat and that major military exercises should be paused to give Kim a chance to prove whether he is “serious.”

Trump announced in Singapore that the US would suspend “war games” with South Korea and Japan, taking Seoul, Tokyo, lawmakers and parts of the US military by surprise.

Additionally, several US defense officials said that, so far, there is no indication that Kim has made good on his promise to return the remains of prisoners of war and soldiers declared missing in action during the Korean War – something Trump has repeatedly said the two leaders agreed upon during their meeting.

These officials also cautioned that a lengthy DNA verification process would be needed when and if any remains are returned to the US.

In South Korea, however, the prism is different. Discussions center less on Trump’s achievements or lack of them, or his failures to live up to his own word, and more on the possibilities his summit opened up – in particular his new relationship with Kim.

“We had great chemistry”

While critics continue to suggest that Trump failed to secure concrete concessions from North Korea – including guarantees related to verifiable irreversible denuclearization and ending human rights abuses – South Korean officials have publicly credited the US President for facilitating the signing of the Panmunjom declaration and the Singapore statement, despite questions over specific terms.

“President Trump has made an unprecedented strategic decision to meet face-to-face with the leader of the DPRK,” Vice Foreign Minister Lim said, noting that Trump accounted for cultural considerations in dealing with Kim by showing him “due respect” and treating “him as a leader of a state.”

“Such friendly gestures created an environment whereby the leaders were able to engage in sincere and candid dialogue on what is an extremely difficult subject,” he said. “Without these leaders and their good chemistry, neither the Panmunjom declaration nor the Singapore statement would have been possible.”

Still, Trump’s warm praise from Kim in the days after the summit continues to raise concerns.

Asked last week why he’s warmed to Kim, Trump insisted he was defusing a nuclear standoff.

“I don’t want to see a nuclear weapon destroy you and your family,” he told reporters during an impromptu question-and-answer session at the White House.

“I want to have a good relationship with North Korea. I want to have a good relationship with many other countries,” Trump said. “We had great chemistry. He gave us a lot.”

On Monday, Pompeo spoke with South Korean Foreign Minister Kang Kyung-wha to “discuss next steps in the wake of the historic Singapore summit,” according to State Department spokesperson Heather Nauert.

And in remarks Monday to the Detroit Economic Club, Pompeo said Kim Jong Un “has made very clear his commitment to fully denuclearize his country” in exchange for promises from the United States including altering the Korean armistice agreement.

Kim, Pompeo said, “has made very clear his commitment to fully denuclearize his country.”

“In return for that, the President has committed to making sure that we alter the armistice agreement, provide the security assurances that Chairman Kim needs,” he added, highlighting the video that Trump showed Kim at the meeting.

“It shows what North Korea could be like,” said Pompeo “… There’s a lot of work to make that, but President Trump is committed to delivering on that part of the bargain as well.”

CNN’s Barbara Starr, Laura Koran, Nicole Gaouette and Nic Robertson contributed to this report