The president made the remarks following a joint signing event with Kim.
With cameras of the world's press trained on them, Trump and Kim built an initial atmosphere of friendship. "The world will see a major change". "Regardless of what happens in that meeting between the two dictators". Trump praised Kim's love of his country, sizing up the strongman as "very talented".
The friendly banter marked the end of one of the most highly anticipated and high stakes diplomatic meetings in a century.
The president acknowledged that US intelligence on the North Korean nuclear stockpile is limited, "probably less there than any other country", he said.
The two men shook hands, posed for the cameras, then walked a short distance before exchanging pleasantries via translators.
During a post-lunch stroll through the gardens of the Singapore hotel where the summit was held, Trump said the meeting had gone "better than anybody could have expected".
"Absolutely I believe this too, and will know within 60 seconds whether I am going to play Trump, or totally play Trump". I think he wants to de-nuke, without that, there's nothing to discuss.
"It was not an easy path here", Kim said.
Kim spoke in Korean, saying that "the old prejudices and practices worked as obstacles on our way forward, but we've overcome all of them, and we are here today".
As the leaders sat down, White House press secretary Sarah Sanders tweeted photos showing the USA and North Korean delegations meeting in a separate room where they watched a video feed showing Kim and Trump together.
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Asked by this reporter whether Kim indeed pledged to denuclearize, something the President promised, Trump insisted the wheels are in motion.
Their agreement also included a commitment from Mr Kim to rid the Korean peninsula of nuclear weapons.
"It's gonna be a great discussion and I think tremendous success".
The meeting marks the first time an American president and Kim have met. Looking forward to a new relationship Trump gave some insights into his conversations with Kim and how the relationship between the US and North Korea soured in the past.
The agreement said the two countries would co-operate towards "new relations" while the United States would provide "security guarantees" to North Korea. "And it's my honor to be involved".
Mr Kim has been accused of horrific rights abuses against his people. Speaking about specifics When asked if there was talk of pulling US troops out of South Korea, Trump said the topic didn't come up. That was, perhaps, until she accidentally called him a dictator.
There were no immediate details on the contents of the document but Trump said he expected the denuclearisation process to start "very, very quickly".
It did not include an agreement to take steps towards ending the technical state of warfare between the USA and North Korea.
"Anthony, talk to us about this moment".
The president, however, did not ignore the North Koreans' history of promises not kept.
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