WASHINGTON -- Like a consummate showman, President Donald Trump began rolling the drum Monday for his summit with North Korean leader Kim Jong Un, suggesting the "big event" take place in the Demilitarized Zone that divides the Koreas. That's where Kim just met his South Korean counterpart.

But Trump said that the Southeast Asian city state of Singapore was also in the running to host what few would have predicted when nuclear tensions were soaring last year -- the first face-to-face meeting between the leaders of the United States and North Korea.

While policy experts, and even his own national security adviser, voice skepticism that North Korea is sincere about giving up its nuclear efforts, Trump sounds like he's gearing up for a date with history, and clearly wants the backdrop to be just right.

First by Twitter, and then at a press conference in the White House Rose Garden, Trump said he likes the idea of going to the southern side of the demarcation line that separates the Koreas, where South Korean President Moon Jae-in met Kim on Friday.

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

There's been much speculation about where Trump and Kim might meet. Countries in Europe and Southeast Asia, in Mongolia and even a ship in international waters have all been suggested as possible venues. Monday was the first time that Trump had publicly named potential locations.

His planned meeting with Kim will be the crucial follow-up to the summit between Kim and Moon on Friday where they pledged to seek a formal end this year to the Korean War -- a conflict that was halted in 1953 by an armistice and not a peace treaty, leaving the two sides technically at war. They also committed to ridding the peninsula of nuclear weapons.

Former reality television star Trump now has to help turn the Korean leaders' bold but vague vision for peace into reality. Undaunted, he gave the impression Monday that governments were vying to host his face-to-face with Kim and share in the attention it would bring.

"Everybody wants us. It has the chance to be a big event," the president said on a bright spring day in Washington, alongside Nigerian President Muhammadu Buhari, whom he'd just met at the White House. "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."

It wasn't clear whether his enthusiasm was stirred by the South Korean president's suggestion Monday that Trump could take the Nobel Peace Prize if the two Koreas win peace. Moon's remark came when he deflected a question about whether he might win the award as one of his predecessors, Kim Dae-jung, did in 2000 after the first ever inter-Korean summit.

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

Trump's recently installed national security adviser, John Bolton, who has in the past advocated military action against North Korea, reacted coolly Sunday to its reported willingness to give up nuclear programs if the United States commits to a formal end to the war and a pledges not to attack.

"We've heard this before," Bolton told CBS' "Face the Nation," adding that the U.S. wanted to see concrete action "not just rhetoric."

This year, Kim has already suspended his nuclear and missile tests. According to South Korean officials, he told Moon that he's going to shut down his country's only known nuclear testing site and allow experts and journalists to observe.

Trump cited that prospect with approval on Monday, saying Kim is "talking about no research, no launches of ballistic missiles, no nuclear testing." But as usual, the president left open the possibility of pulling the plug on talks, saying: "If it's not a success, I will respectfully leave.