He says much more work has been done by the US and North Korean teams that couldn't be encapsulated in the Trump-Kim Jong Un statement. So he says teams will now work to make more progress on those items.
Trump lashed out at media coverage of his meeting with North Korean dictator Kim Jon Un, some of which has raised questions about how much was gained during the meeting in Singapore.
"Our country's biggest enemy is the Fake News so easily promulgated by fools!" Trump wrote, claiming that television networks "are fighting hard to downplay the deal with North Korea."
Trump's tweets followed a high-profile summit which yielded a renewed promise by Kim to "denuclearise" the Korean Peninsula but was scant on details. Lawmakers, analysts and allies have hailed the effort but questioned the substance of what was achieved.
The President's tweets began shortly after Air Force One landed at Joint Base Andrews just outside Washington and continued once he reached the White House.
In one tweet, Trump said that North Korea is no longer the United States' most dangerous problem, as President Barack Obama had characterised it upon leaving office - and he said Americans could "sleep well tonight!"
His assessment was ridiculed by Democratic lawmakers and some analysts, who suggested that North Korea remains a serious threat.
"This is truly delusional," Senator Chris Van Hollen, (D), wrote on Twitter. "It has same arsenal today as 48 hours ago. Does he really think his big photo-op ended the DPRK's nuclear programme? Hope does not equal reality."
Congressman Adam Schiff, (D), also mocked Trump, writing: "One trip and it's 'mission accomplished,' Mr President?"
"North Korea is a real and present threat," Schiff said in a tweet. "So is a dangerously naive president."
Richard Haas, the president of the Council on Foreign Relations, said "the summit changed nothing."
"Worse yet, overselling the summit makes it harder to keep sanctions in place, further reducing pressure on NK to reduce (much less give up) its nuclear weapons and missiles," Haas wrote on Twitter.
A brief document signed by Trump and Kim provided virtually no detail beyond the stated commitment to "denuclearise," a promise that Pyongyang has made and ignored many times.
In his tweets, Trump also defended a major concession made to North Korea while he was in Singapore: that the United States would halt joint military exercises with South Korean forces on the Korean Peninsula.
"We save a fortune by not doing war games, as long as we are negotiating in good faith - which both sides are!" the President wrote.
In earlier tweets, Trump called his meeting with Kim "an interesting and very positive experience."
He also said that before he took office last year, "people were assuming that we were going to war with North Korea."
"President Obama said that North Korea was our biggest and most dangerous problem. No longer - sleep well tonight!" the president wrote.
Obama, as he left office, warned Trump that the North Korean nuclear and missile programmes were likely to be the most urgent problem he would confront, according to a March New York Times report.
Trump, who has frequently sparred with the media, was also unsparing in his criticism of television coverage of the summit, singling out two networks for scorn.
"So funny to watch the Fake News, especially NBC and CNN," he wrote on Twitter. "They are fighting hard to downplay the deal with North Korea. 500 days ago they would have 'begged' for this deal-looked like war would break out. Our Country's biggest enemy is the Fake News so easily promulgated by fools!"
Even as they offered measured praise for Trump's diplomatic efforts, congressional Republicans have emphasised the difficult road that remains and pressed for more details of what exactly the President agreed to with Kim.
Senator Bob Corker, (R) said yesterday that he wants Pompeo to brief senators on the substance of what the two nations discussed, including whether US troops stationed on the Korean Peninsula would remain.
"I have no idea" whether Trump secured anything of substance, said Corker, the retiring chairman of the Senate Foreign Relations Committee. "At this juncture, I don't think we know enough to challenge or celebrate."
At a news conference in Singapore after nearly five hours of talks there with Kim, Trump said he "knows for a fact" that North Korea is serious about denuclearization this time and that Kim "wants to do the right thing." The work of putting meat on the bare bones of the agreement will begin quickly, he said, and "once you start the process, it means it's pretty much over."
Talks are to be led on the U.S. side by Pompeo and, according to the agreement, a "relevant, high-level" North Korean official. But no specifics of a future path were outlined. There was no mention of a declaration of North Korea's nuclear assets, which normally precedes any arms-control negotiation, or of timelines or deadlines.
- additional reporting AP
