The United States President Donald Trump and North Korea Leader Kim Jong-un have signed a document described by the American leader as important and comprehensive, following a historic summit between the two in Singapore, The document that many analysts called it doubtful deal.

The meeting was the first between a sitting U.S. president and a North Korean leader.

The meeting began at 9 a.m. on Tuesday local time on Singapore's Sentosa Island at the Capella Hotel, a former British colonial barracks converted into a high-end hotel, starting with a carefully choreographed handshake greeting against a backdrop of the U.S. and North Korean flags.

The Trump-Kim historic summit on June 12, 2018, seemed unthinkable months ago.

After meeting privately and with aides, Trump and Kim moved into the luncheon at a long flower-bedecked table.

Trump and Kim arrived in Singapore on Sunday to hold the first ever face-to-face meeting between leaders of the two countries, which have remained enemies since the 1950-1953 Korean War.

Trump was scheduled to return to the United States on Wednesday, but will now leave immediately after meeting with North Korean leader Kim on Tuesday, the White House said in a statement on Monday.

Earlier, the White House said Trump will leave Singapore on Tuesday night, adding that nuclear talks with North Korea are moving “more quickly than expected.”

The U.S. president reportedly moved up his departure time from Singapore after Kim set the deadline for their historic summit. Bloomberg News reported on Monday that Kim will leave Singapore at 4 p.m. on Tuesday local time after his meeting with Trump.

The meeting & the handshake

The two leaders addressed the media before walking into their one-on-one discussion. Trump said he is confident the talks will be a “tremendous success” and that “we will have a tremendous relationship, I have no doubt”.

The U.S. president said he had formed a “very special bond” with Kim and that the U.S.’s relationship with Pyongyang would be very different.

“People are going to be very impressed and people are going to be very happy and we are going to take care of a very dangerous problem for the world,” he added.

Asked whether he would invite Kim to the White House, Trump answered, “Absolutely, I will”, adding Kim accepted his invitation to visit the White House at the “appropriate” time.

Kim said that “it has not been easy to get here” and that “the old prejudices and practices worked as obstacles, but we have overcome them and we are here today.”

“Many people in the world will think of this as a form of fantasy from a science fiction movie,” the North Korean leader said, according to pool reporters.

Both leaders expressed optimism throughout roughly five hours of talks, with Trump thanking Kim afterward “for taking the first bold step toward a bright new future for his people.”

Trump added during a news conference that Kim has before him “an opportunity like no other” to bring his country back into the community of nations if he agrees to give up his nuclear program.

As both leaders stood on a hotel veranda to say their final goodbyes, Trump said: “We'll meet again. We will meet many times.”

After the signing, Trump said he expected to “meet many times” in the future with Kim. For his part, Kim hailed the “historic meeting” and said they “decided to leave the past behind.”

Trump had said before leaving for the summit that he would be able to tell within minutes whether he'd be able to strike a deal with Kim to dismantle the North's nuclear program.

The optimistic summit was a remarkable change in dynamics from less than a year ago, when Trump was threatening “fire and fury” against Kim, who in turn scorned the American president as a “mentally deranged U.S. dotard.” Beyond the impact on both leaders’ political fortunes, the summit could shape the fate of countless people — the citizens of impoverished North Korea, the tens of millions living in the shadow of the North’s nuclear threat, and millions more worldwide.

Trump and Kim sign agreement after historic summit

Trump and Kim capped a one-day peace summit by signing the agreement without immediately disclosing the terms. Trump stayed on to detail the agreement at a later news conference while Kim left the summit for a return flight to Pyongyang.

Trump and Kim signed an agreement on Tuesday pledging to support a peaceful resolution to seven decades of hostilities between the two countries and a de-escalation of nuclear tensions.

Under the agreement, the U.S. committed to provide security guarantees to its old enemy while North Korea “commits to work towards complete denuclearization of the Korean Peninsula”.

That provision falls short of the hoped-for “complete, verifiable, irreversible denuclearization” of North Korea that had been urged by the U.S. and its allies in the build-up to Tuesday's talks.

Trump defended the agreement at a press conference on Tuesday afternoon, saying both he and Kim are committed to its provisions.

“Today is the beginning of an arduous process,” Trump told reporters. “Our eyes are wide open, but peace is always worth the effort, especially in this case.”

Trump said economic sanctions against the country will remain in effect until North Korea reverses its nuclear program, and added there are no short-term plans to reduce the number of the U.S. troops - some 28,500 - stationed in South Korea.

Before signing the document, Kim said the two leaders had had a historic meeting “and decided to leave the past behind. The world will see a major change.”

 Four major points covered in the Trump-Kim agreement:

The U.S. and North Korea will pursue better relations “in accordance with the desire of the peoples of the two countries for peace and prosperity”.

The U.S. and North Korea “will join their efforts to build a lasting and stable peace” on the Korean Peninsula.

North Korea commits to “work towards denuclearization”.

The countries agree to recover and repatriate prisoners of war (POWs) and missing in action (MIA) remains dating back to the Korean War.

The flip side to the summit coin

Analysts are divided over the agreement, with some saying it does nothing to avoid repeating past mistakes in similar attempts at a denuclearization deal.

Others see the summit as a welcome reversal to decades of hostility and harsh language between the U.S. and North Korea.

While the summit is seen as a test for diplomacy that could end the long-running nuclear standoff, foreign policy experts say the stakes are high if it does not result in a nuclear agreement.

Experts say the talks could run into trouble because the U.S. and North Korea hold different understandings of what it means for the latter to denuclearize.

Critics of the summit leapt at the leaders’ handshake and the moonlight stroll Kim took on Monday night along the glittering Singapore waterfront, saying it was further evidence that Trump was helping legitimize Kim on the world stage. Kim has been accused of horrific rights abuses against his people.

Giving voice to the anticipation felt around the world as the meeting opened, South Korean President Moon Jae-in said on Tuesday he “hardly slept” before the summit. Moon and other officials watched the live broadcast of the summit before a South Korean Cabinet meeting in his presidential office

Trump blasts 'haters & losers'

Meanwhile, about three hours before the summit Trump blasted the “haters & losers” who have expressed skepticism about its success.

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

Trump: North Koreans very working people who love their leader

Elsewhere, Trump said North Koreans are very working and industrious people and they “love” their leader Kim Jong-un.

“His country does love him,” Trump said in an interview with ABC News following the historic summit between Trump and Kim in Singapore.

The U.S. president said “you see the fervor” the North Koreans have for their leader.

“They're gonna put it together, and I think they’re going to end up with a very strong country, and a country which has people  — that they’re so hard working, so industrious,” Trump said.

Trump told ABC News that Kim “wants to do the right thing” and that begins with denuclearization.

Pompeo’s threat

Earlier on Monday, the U.S. Secretary of State Mike Pompeo issued a stern warning ahead of the historic summit.

He told reporters in Singapore that the United States will not lift economic sanctions against North Korea until Pyongyang fully eliminates its nuclear weapons capability.

A complete, verifiable and irreversible denuclearization “is the only outcome that the United States will accept,” Pompeo said. “If diplomacy doesn’t move in the right direction, sanctions will increase.”

“We’re ready for today,” Pompeo said in a tweet sent out on Monday morning with a photo of him leaving the Singapore hotel where the U.S. delegation is staying.

Alluding to the North’s concerns that giving up its nuclear weapons could surrender its primary deterrent to forced regime change, Pompeotold reporters that the U.S. was prepared to take action to provide North Korea with “sufficient certainty” that denuclearization “is not something that ends badly for them.”

He would not say whether that included the possibility of withdrawing the U.S. troops from the Korean Peninsula, but said the U.S. was “prepared to take what will be security assurances that are different, unique, than America’s been willing to provide previously.”

The North has faced crippling diplomatic and economic sanctions as it has advanced development of its nuclear and ballistic missile programs. Pompeo held firm to Trump’s position that sanctions will remain in place until North Korea denuclearizes — and said they would even increase if diplomatic discussions did not progress positively.

Trump and Kim have yet to agree even on how to define denuclearization of the Korean Peninsula.

The U.S. seeks the complete and irreversible dismantling of North Korea’s nuclear program. Pyongyang is demanding a solid guarantee of its security and the removal of Washington’s nuclear umbrella protecting allies South Korea and Japan.

The North has also sought an end to the U.S. military presence in the South, where Washington has around 28,000 troops.

So far the U.S. has failed to provide details on what kind of security guarantees it is prepared to offer.

Trump acknowledged that the timetable for denuclearization is long, but said, “Once you start the process it means it’s pretty much over.”

U.S., North Korea delegations sit down for talks

Shortly after the one-on-one meeting between Kim and Trump, White House Press Secretary Sarah Huckabee sanders announced on her Twitter account that North Korean and American delegations had started talks as well.

 Trump says to end ‘expensive’, ‘provocative’ war games with South Korea

Elsewhere, Trump said the United States was stopping “very provocative” and expensive military exercises with South Korea to facilitate denuclearization negotiations with North Korea.

The United States and South Korea hold regular military drills to the fury of North Korea, which has long seen the drills as preparations to invade it.

“The war games are very expensive, we pay for the majority of them,” Trump told a news conference on Tuesday in Singapore after a historic summit with North Korean leader Kim Jong-un.

“Under the circumstances, that we’re negotiating ... I think it’s inappropriate to be having war games.”

Check out my ride: Trump shows Kim Jong Un ‘The Beast’

Trump offered Kim a rare glimpse inside the presidential limousine known as “The Beast” on Tuesday as their historic summit in Singapore wound down.

After meetings and a working lunch, Trump and Kim were spotted approaching Trump's hulking black limousine, adorned with an American flag. Trump gestured to the car and then a Secret Service agent opened the right passenger door.

Kim could be seen smiling as the two stood chatting and Kim peeked inside.

While there was initially some confusion about what the leaders were doing, it quickly became clear that Trump was making a classic alpha male move: showing Kim his ride.

 Dennis Rodman weeps with joy over Trump-Kim summit

The U.S. NBA (National Basketball Association) Hall of Famer Dennis Rodman gave an emotional, bizarre TV interview on Tuesday reacting to the highly anticipated summit between Trump and Kim.

Wearing a red “Make America Great Again” hat and sunglasses, Rodman, who has personally visited North Korea multiple times, spoke for roughly 20 minutes about his relationship with Kim and his expectations for the historic meeting between the two leaders as it got underway in Singapore. He began to cry about halfway through the interview, periodically dabbing his nose with a tissue.

Rodman found himself in a rare position as the summit came together, having met both leaders. He appeared on Trump's television show, “Celebrity Apprentice,” and has made several trips to North Korea.

On Monday, Rodman talked about “falling in love” with the people and culture of North Korea, and described Kim as “a good friend.”

“This guy wants to be around the world,” he said. “He wants to come to America and enjoy his life. He wants his people to enjoy this life.”

Rodman said Kim understands “bits and pieces of English,” and described him as “more like a big kid even though he is small.”

Rodman became particularly emotional as he recalled returning home from his from first trip to North Korea. He said he was chastised for making the trip, and was rebuffed by the White House when he sought to relay messages from Kim to then-President Barack Obama.

Rodman says he received a call from the White House ahead of Trump's historic meeting with North Korean leader Kim Jong-un.

Rodman told CNN in an interview from Singapore on Tuesday that a White House staffer called the former “Celebrity Apprentice” contestant to tell him the president was proud of him.