President Donald Trump declared the Kim Jong Un summit an historic success Tuesday that will lead to the denuclearization of North Korea, even as critics pointed out that a joint statement signed by the leaders lacks specifics.

"Today is the beginning of an arduous process — our eyes are wide open," Trump said at a news conference following the unprecedented meeting with the North Korea dictator.

Trump also said he would not withdraw U.S. troops from South Korea as part of the agreement, though he would like to "get our soldiers home" at some point. Trump also said the U.S. would stop "war games" military exercises with South Korea, saying they are too expensive and "provocative."

While there will be "vigorous negotiations" on denuclearization, Trump said he believes Kim is "very talented" and will follow through on his pledge to disarm in exchange for economic assistance. At another point, however, Trump say "I may be wrong" about his new negotiating partner.

"We'll probably need another summit," Trump said during the news conference that lasted more than an hour.

Trump spoke as numerous foreign policy analysts pointed out that Trump-Kim agreement cites only intentions to denuclearize, with no specifics about how to get that done. The agreement says nothing about verification or inspection systems to make sure North Korea actually gets rid of weapons.

"The summit was heavy on pomp and circumstance and low on details," said Olivia Enos, policy analyst with the Asian Studies Center at The Heritage Foundation in Washington.

The pledge on denuclearization did not include the U.S. demands for a "complete, verifiable, irreversible dismantlement" of North Korea's nuclear weapons programs, she pointed out.

"The promise of future dialogue means its possible to hammer out those details going forward, but commitments were limited, general and unspecific," said Enos, who was in Singapore for the summit.

The general agreement also did not provide specifics about what Kim means by "denuclearization." In the past, North Korea has said it requires the U.S. to pull back its own nuclear weapons systems in the region, as well as withdraw American troops from South Korea.

The agreement "is even thinner than most skeptics anticipated," tweeted Robert E. Kelly, a political science professor at Pusan National University in South Korea, tweeted that

Kelly said he figured Trump would "at least get some missiles or a site closure or something concrete."

During his news conference, Trump said that Kim told him he would soon destroy a nuclear test site. He again expressed confidence that Kim would surrender his nuclear weapons in exchange for economic assistance that would improve his country's standard of living.

Trump had nicer things to say about Kim than about some of the western allies he met with over the weekend at the G-7 summit in Canada, particularly Canadian Prime Minister Justin Trudeau. The president said some of those allies are taking advantage of the United States on Trump, and that he responded harshly to Trudeau because the prime minister had criticized him after the G-7 meetings.

Asked about Kim's sincerity, Trump said no one can be certain of anything, but "we're going to be certain soon" about Kim's intentions pursuant to ongoing negotiations.

As the summit wrapped up, administration officials said they gave Kim and his aides a film outlining the choices facing North Korea.

"There can only be two results," the film said: "One of moving back and one of moving forward" — and "it illustrated the "moving back" option with clips of missiles firing.

Trump said his staff showed the film to Kim, and "I think he loves it."

In a post-summit interview with ABC News, Trump said the agreement provides a "framework for getting ready to denuclearize," and he said he trusts Kim to follow through.

"I've met him, I've spoken with him ... He really wants to do a great job for North Korea," Trump said. "I think he wants to de-nuke. Without that there's nothing to discuss."