President Donald Trump on Monday floated the idea of holding his planned summit with North Korean leader Kim Jong Un in the Demilitarized Zone that divides the Koreas.

That's where South Korean President Moon Jae-in met Kim on Friday, the first time a North Korean leader has visited south of the demarcation line that divides the rival nations.

"There's something that I like about it because you are there, you are actually there," Trump said at a news conference in the White House Rose Garden. "If things work out there's a great celebration to be had on the site, not in a third-party country."

A Trump-Kim meeting would be the first U.S.-North Korean leadership summit in more than six decades of hostility since the 1950-53 Korean War. Trump has previously said that five locations were being considered, but on Friday said the choice had been narrowed to two or three.

Monday was the first time he'd publicly specified potential locations for the meeting, slated for May or early June. He added that the Southeast Asian city state of Singapore was also in the running.

There's been rampant speculation since Trump accepted the offer from Kim for direct talks on where would be an acceptable venue to both sides. Countries in Europe, Southeast Asia, and Mongolia or even a ship in international waters have all been suggested as possible venues.

Trump on Monday made it sound like governments were vying to play host.

"Everybody wants us. It has the chance to be a big event," the president said alongside Nigerian President Muhammadu Buhari, whom he met at the White House Monday.

"The United States has never been closer to potentially have something happen with respect to the Korean Peninsula that can get rid of the nuclear weapons, can create so many good things, so many positive things, and peace and security for the world," Trump said.

True to form, he had first aired his thoughts on the summit venue in the early morning via Twitter, suggesting the Peace House and Freedom House on the southern side of the DMZ would be a "Representative, Important and Lasting site."

Trump on Friday claimed credit for the inter-Korean summit, which has spurred hopes of peace on the Korean Peninsula after a torrid 2017 when North Korea rapidly advanced its development of nuclear weapons and ballistic missiles. The president now faces a burden in helping turn the Korean leaders' bold but vague vision for peace into reality.

The United States has reached aid-for-disarmament deals with North Korea before. The most enduring effort negotiated by the Bill Clinton administration 1994 halted the North's production of plutonium for nearly a decade but collapsed over suspicions that it had a secret program to enrich uranium giving it an alternative route to make fissile material for bombs.

Setting aside generations of animosity, Kim and Moon on Friday pledged to seek a formal end to the Korean War by year's end and to rid the peninsula of nuclear weapons.

South Korean officials cited Kim as saying he would be willing to give up his nuclear programs if the United States commits to a formal end to the war and a pledge not to attack the North. Kim had already suspended his nuclear and missile tests while offering to put his nukes up for negotiations. Seoul says he's willing to shut down his country's only known nuclear testing site and allow outside experts and journalists to watch the process. But there is still deep skepticism over whether Kim is truly willing to negotiate away the nukes that his country has built after decades of struggle.

Trump on Monday repeated his complimentary appraisal of North Korea's current dictator Kim, whom just a few months ago he lampooned as "Little Rocket Man" when fears of a war ran high.

"Maybe a lot of things change, but Kim Jong Un ... has been very open and very straightforward so far," Trump said." I can only say again so far, but he's talking about getting rid of the site, which was their big site, he's talking about no research, no launches of ballistic missiles, no nuclear testing and he's lived up to that for a long period of time." The North's last missile test was in November.

Trump sounded confident that the summit would take place and would be a success, but left open the possibility of pulling the plug on talks, saying: "If it's not a success, I will respectfully leave."

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Associated Press writer Catherine Lucey contributed to this report.