WASHINGTON -- South Korean President Moon Jae-in and North Korean leader Kim Jong Un pledged on Friday to work toward denuclearizing the Korean Peninsula and declaring a formal end to the Korean War by the end of the year. National security experts, and even the South Korean foreign minister, are crediting President Trump for bringing North Korea to the table.

Now, Mr. Trump faces a burden in helping turn the Korean leaders' bold but vague vision for peace into reality after more than six decades of hostility. Mr. Trump must contend with two nagging suspicions: first about his own suitability to conduct that kind of war-and-peace negotiation and succeed where his predecessors have failed; secondly, whether North Korean leader Kim Jong Un really is willing to give up the nuclear weapons his nation took decades acquiring.

"It is still unclear whether North Korea still believes that it can have its cake and eat it too," said Victor Cha, who until January had been in the running to become Mr. Trump's choice for ambassador to South Korea. Cha said that while the atmospherics of the inter-Korean summit got an "A'' grade, the meeting had failed to clarify whether Kim is willing to give up his nukes or is interested in just freezing his programs in return for sanctions relief and economic and energy assistance.

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At a White House news conference with German Chancellor Angela Merkel on Friday, Mr. Trump basked in the afterglow of the feel-good meeting between Kim and South Korean President Moon Jae-in, and said he has a responsibility to try to achieve peace and denuclearization.

"And if I can't do it, it'll be a very tough time for a lot of countries, and a lot of people. It's certainly something that I hope I can do for the world," he said.

While Moon and Kim pledged to seek a formal end to the Korean War by year's end and to rid their peninsula of nuclear weapons, they didn't specify how it would be achieved. And now the pressure to deliver results, at least on the allies' side, has shifted to Mr. Trump.

"There will be a suggestion that the South Koreans have teed it up very well for him and he's not going to have the option of walking away in a huff," said Christopher Hill, who was the lead U.S. negotiator with North Korea under the George W. Bush administration.

Mr. Trump left little doubt the unprecedented U.S.-North summit, tentatively scheduled for May or early June, will go ahead. He said he was looking forward to the meeting and that it "should be quite something."

Mongolia and Singapore are the final two sites under consideration for the upcoming summit, two administrative sources told CBS News' Major Garrett. Mr. Trump told reporters Friday that the location had been narrowed down to two spots.

The president pushed back against critics that say he's being manipulated by Kim, who has abruptly shifted to diplomacy after last year's full-scale push to become a nuclear power that could threaten the U.S. mainland.

"I don't think he's ever had this enthusiasm for somebody, for them wanting to make a deal," Mr. Trump said in the Oval Office. "We're not going to be played, OK. We're going to hopefully make a deal. The United States in the past has been played like a fiddle."

New Secretary of State Mike Pompeo, who as then-CIA director met Kim four weeks ago in North Korea, told reporters in Brussels that he got the impression that Kim was "serious" about negotiating on denuclearization because of the Trump-led economic pressure campaign.

But Pompeo added a word of caution: "I am always careful. There is a lot of history here. Promises have been made, hopes have been raised and then dashed."

North Korea has already called a halt to nuclear and long-range missile tests, which has helped dial down tensions significantly. But Mark Fitzpatrick, the Washington-based executive director of the International Institute for Strategic Studies, said the promise of denuclearization must now be backed by tangible actions, like an end of North Korean production of fissile material that can be used for bombs and the dismantling of nuclear facilities.

Hill, the former U.S. negotiator, said the key hurdles for the Trump administration would be to set a timetable for denuclearization and overcome North Korean reluctance to allow a verification process -- a failing of past aid-for-disarmament deals.

"I'm guided by my experience which was they said all the right things but they gave us a declaration that was not complete and not entirely accurate, and they also failed to give us any kind of verification protocol," he said.

Despite the optimism, Mr. Trump reiterated Friday that the U.S.-led pressure campaign could continue "until denuclearization occurs."

North Korea was hit with unprecedented economic restrictions during a feverish 2017, when the U.S. and North Korean leaders traded threats while Kim pushed his nation to the verge of being able to fire a nuclear-tipped missile at the U.S. mainland.

The diplomatic climate has changed dramatically this year, as Kim has ended his international seclusion, reaching out to South Korea, the U.S., and China.

Defense Secretary Jim Mattis said the U.S. is "optimistic right now that there's opportunity here that we have never enjoyed since 1950" and any progress will be up to the diplomats. He was referring to the year the Korean War broke out.

The fighting, which also involved China, halted three years later after hundreds of thousands of lives had been lost, through the declaration of an armistice, not a peace treaty. That has left the peninsula in a technical state of war for more than six decades.