The two leaders met on Tuesday, signing a brief declaration on denuclearisation and reducing tensions.
The president tweeted after returning from his Singapore summit that "the Fake News, especially NBC and CNN", are "fighting hard to downplay the deal with North Korea". So a Trump deal presumably would not only eliminate North Korea's current nuclear warheads, which are estimated to be at about 60, but prohibit further production forever - and end Pyongyang's militaristic programs like providing weapons to Syria and its horrific violations of human rights.
He also said that before he took office a year ago, "people were assuming that we were going to War with North Korea".
The Pentagon has since sought to reassure its allies of its "ironclad" security commitments.
"It's important that we don't lose sight of the fact that Kim Jong Un is a butcher and he is a butcher of his own people", Sen.
Mr. Trump also claimed Kim told him North Korea has destroyed a "major" missile testing site, although he didn't expand on that.
No fewer than 14 images of his visit to the Marina Bay Sands (MBS) hotel, casino and convention centre and other sights were printed on the front page of the state-run Rodong Sinmun newspaper.
State media agency KCNA published an enthusiastic article in English praising the talks as a historic break from the past.
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KCNA also asserted Trump had "expressed his intention" to lift sanctions against the North - something the U.S. president had said would happen "when we are sure that the nukes are no longer a factor".
In a news conference after the summit, Trump said that USA sanctions against the North may be lifted earlier than expected.
He also announced that the United States will stop conducting military drills with South Korea after the historic summit, something widely seen as a concession as Pyongyang has long claimed they are invasion rehearsals.
The administration's argument is that the incremental approach used by past administrations has allowed North Korea to extract rewards and incentives from the USA, only to ultimately renege and refuse to give up its nukes.
North Korea's state media hailed the summit as a success, including highlighting Trump's surprise announcement after the meeting that the USA would stop military exercises with South Korea, which the North has long sought. "We'll be verifying", the president remarked in a rare, extended news conference after the summit. He also said he hoped that this would be soon.
KCNA also reported that both leaders had agreed to visit each other in the USA and North Korea respectively.
Sen. Bob Corker (R-Tenn.) said Tuesday that he wants Secretary of State Mike Pompeo to brief senators on the substance of what the two nations discussed, including whether USA troops stationed on the Korean Peninsula would remain.
"It is up to the US and South Korea to decide about their joint exercises. We are not going to let that happen, and he's got to get the message that something's got to change", Lamborn said. But the two countries didn't nail down how and when the North might denuclearize or shed light on the unspecified "protections" Trump pledged to Kim and his government.
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