SINGAPORE — President Donald Trump and North Korean dictator Kim Jong Un shook hands on Tuesday morning — a historic first meeting between leaders of the two nations — as they opened a one-day summit that U.S. officials hope ultimately will result in Kim giving up his nuclear program.

As the two men approached each other on a colonnade at the Capella Hotel on Sentosa Island here, with American and North Korean flags interspersed behind them, reporters could hear Kim say, "Nice to meet you, Mr. President."

Then, the two men posed for photographs, stern-faced, before making their way to a meeting room where they spoke briefly to the media.

"We will have a terrific relationship," Trump said. "I have no doubt."

Kim noted the nascent relationship already has survived serious obstacles — this meeting was planned, canceled and put back on the calendar — in getting to the point where the leaders could talk with each other in person.

"It was not easy to get here," but the two sides "overcame" obstacles, the North Korean leader said through a translator.

"That's true," Trump replied.

Trump hyped the drama surrounding the tête-à-tête a few hours before the handshake, tweeting that "we will all know soon" if a "real deal" is in the offing.

He has placed his emphasis on the personal dynamics of the relationship he forges with Kim, whom American officials say will have to give up his nuclear arsenal and his ability to develop new weapons in order to get relief from crippling U.S. economic sanctions and assurances that the U.S. will not take military action against him.

The president headed to the meeting after staff-level talks between the two nations "moved more quickly than expected" in recent days, the White House said.

"The fact that I am having a meeting is a major loss for the U.S., say the haters & losers," Trump also tweeted shortly before the meeting. "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!"

Before arriving here, Trump said it wouldn't take him long to gaugewhether Kim is just looking for a photo-op or is willing to make the kinds of concessions that would end North Korea's decades of isolation.

"I think within the first minute, I'll know — just my touch, my feel," Trump said recently.

The two leaders' schedule called for a sit down for a meeting at which the only other people in the room would be translators. After that, they were expected to participate in a larger bilateral dialogue along with North Korean officials, Secretary of State Mike Pompeo, White House chief of staff John Kelly and national security adviser John Bolton. And they were set to wrap up their time together with a working lunch.

Pompeo and Bolton have played the good cop/bad cop roles in the administration's negotiations with Pyongyang. Pompeo has previously met with Kim and, as the nation's top diplomat, has a lot invested in striking a deal. Bolton raised eyebrows last month when he began openly discussing using a "Libya model" in negotiations with Kim.

When Bolton worked in President George W. Bush's administration, Libyan leader Moammar Gadhafi gave up his nuclear program under the threat of U.S. military action against him and the promise of sanctions relief. To that point, the parallel could be appealing to Kim.

But Gadhafi ended up dead within a decade following a U.S.-led bombardment of his country. Bolton's use of the Libya phrasing, reiterated by Vice President Mike Pence in an interview, contributed to a tiff between the two nations and the brief cancellation of the summit by Trump. But it was quickly put back on track.

Trump is expected to wrap up his stay in Singapore with a news conference before leaving Tuesday night to return to Washington.