President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE met with North Korean leader Kim Jong Un in Singapore, a historic encounter that Trump hopes will lead to a lasting peace agreement and the dismantling of North Korea’s nuclear program.

The first-ever meeting between a U.S. president and a North Korean leader began just after 9 a.m. Tuesday local time with a handshake, producing images that were carried live on television across the United States and beyond.

Kim and Trump exchanged pleasantries before the two men turned on the red carpet to pose for photos in front of a line of U.S. and North Korean flags.

After Trump sat down next to Kim for their meeting inside the swanky Capella Hotel, the president predicted he would have a “terrific relationship” with the North Korean leader.

“I feel really great,” Trump said. “It's going to be a great discussion and, I think, tremendous success.”

Kim said through a translator, "The past worked as fetters on our limbs, and the old prejudices and practices worked as obstacles on our way forward. But we overcame all of them, and we are here today.”

The two men spoke one-on-one for roughly 45 minutes with only translators present before heading into broader meetings with their advisers. Trump said their initial meeting was “very, very good” and that he and Kim have a “excellent relationship.”

In the wider huddle, Trump predicted he and Kim “will solve a big problem, a big dilemma” regarding North Korea’s nuclear program. The president was flanked by White House chief of staff John Kelly John Francis KellyMORE, Secretary of State Mike Pompeo Michael (Mike) Richard PompeoTreasury sanctions individuals, groups tied to Russian malign influence activities Navalny released from hospital after suspected poisoning Overnight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers MORE and national security adviser John Bolton.

The leaders and their staff were set to continue the discussion over a lunch of prawn cocktail and avocado salad, green mango kerabu with fresh octopus, beef short rib confit, crispy pork, soy-braised cod and Häagen-Dazs ice cream.

Trump emerged from the meeting saying things went “better than anybody could have expected” and added he and Kim are “going right now for a signing.”

It was not immediately clear what the leaders would be signing.

The summit was unimaginable just last year, when the world was on edge about the possibility of nuclear war as the two leaders hurled personal insults at each other and Kim conducted weapons tests.

Behind the smiles and handshakes, however, Trump and his team of advisers have sent mixed signals about their expectations for the summit’s outcome.

Trump tweeted early Tuesday morning in Singapore that “we will all know soon” whether he can broker a deal with Kim that would help stave off the threat of nuclear war.

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“Meetings between staffs and representatives are going well and quickly ... but in the end, that doesn’t matter. We will all know soon whether or not a real deal, unlike those of the past, can happen!”

Even before the meeting, the president framed his interactions with Kim as a success.

“The fact that I am having a meeting is a major loss for the U.S., say the haters & losers,” Trump tweeted. “We have our hostages, testing, research and all missle [sic] launches have stoped [sic], and these pundits, who have called me wrong from the beginning, have nothing else they can say! We will be fine!”

Critics have said Trump conceded too much to North Korea by granting their leader an in-person meeting.

Others have expressed concern the president has not done enough to prepare for the summit, which was hastily arranged over the course of just three months.

The president told reporters at last weekend’s Group of Seven summit that he will know “within the first minute” whether Kim is serious about denuclearizing.

Trump boasted earlier in a meeting with Japan’s prime minister, who is concerned about the talks, that he does not have to prepare “very much” to meet with Kim because he believes “it’s about attitude.”

“Just my touch, my feel. That's what I do,” he said when asked how he will know.

Days before the talks, Trump raised the possibility he could reach a nuclear deal with Kim or work on an agreement to end the Korean War during the summit. He even said the meeting could be extended by one or two days.

But the White House abruptly announced Monday that Trump would leave Singapore on Tuesday evening local time, leaving him just a few hours to meet with Kim.

The White House said the discussions have “moved more quickly than expected” in explaining the schedule change, but reports later emerged that Kim decided to cut the meeting short, prompting Trump to move up his departure time.

The meeting stood in stark contrast to last year, when Trump mounted a “maximum pressure” campaign of sanctions and diplomatic pressure on Kim while threatening to rain “fire and fury” on the reclusive North Korean leader if he threatened the U.S. with a nuclear strike.

Kim responded by calling Trump a “mentally deranged … dotard” and boasting about his nuclear arsenal.

The two men still have a wide diplomatic gap to bridge before a deal is reached, including a lingering dispute over the definition of denuclearization.

U.S. officials have said North Korea must commit to surrounding their weapons program in a verifiable, permanent way in order to get sanctions relief and promises of protection, but Pyongyang has balked at those demands.

Pompeo the day before the summit stressed the U.S. is prepared to offer Kim “unique” security assurances.

“We’re prepared to take actions that will provide them sufficient certainty that they can be comfortable that denuclearization isn’t something that ends badly for them,” he told reporters. “Indeed, just the opposite: that it leads to a brighter, better future for the North Korean people.”

The gulf between the U.S. and North Korea had led to an escalating war of words that led Trump to call off the summit just over two weeks ago.

Trump wrote a letter to Kim on May 24 blaming Pyongyang's “tremendous anger and open hostility” toward Washington for the summit's cancellation.

But Trump announced the summit was back on just one week later after meeting with Kim's right-hand man in Washington.

The president cautioned it could take multiple meetings to broker a deal.

“It will be a beginning,” he said of the summit. “I've never said it happens in one meeting.”

— Updated at 12:46 a.m.