U.S. President Donald Trump shakes hands with North Korea leader Kim Jong Un at the Capella resort on Sentosa Island, June 12, 2018 in Singapore.
U.S. President Donald Trump shakes hands with North Korea leader Kim Jong Un at the Capella resort on Sentosa Island, June 12, 2018 in Singapore.

SINGAPORE - U.S. President Donald Trump said his historic meeting Tuesday in Singapore with North Korean leader Kim Jong Un went “better than anybody could have expected.”

The two leaders walked outside together after a working lunch with delegations from their respective sides, a session that followed about 40 minutes of talks that included only Trump, Kim and their translators.

“We had a really fantastic meeting, a lot of progress, very positive,” Trump said. He added, “We’re going right now for a signing,” without specifying what exactly would be signed.

WATCH: Trump, Kim Emerge From Working Lunch

Trump and Kim traveled to Singapore to chiefly discuss the possible denuclearization of the Korean Peninsula.

At their lunch meeting, the U.S. side included Secretary of State Mike Pompeo, National Security Adviser John Bolton and White House Chief of Staff John Kelly.The North Korean participants included former military intelligence chief Kim Yong Chol, Minister of Foreign Affairs Ri Yong Ho, and Ri Su Yong, vice chairman of the ruling Workers’ Party.

“We will solve a big problem,” Trump said ahead of the main talks.

U.S. President Donald Trump and North Korea's lead
U.S. President Donald Trump and North Korea's leader Kim Jong Un shake hands during an expanded bilateral meeting at the Capella Hotel on the resort island of Sentosa, Singapore, June 12, 2018. With them are Senior North Korean Diplomat Ri Su Yong, top left, and White House Chief of Staff John Kelly, top right.

Tuesday’s unprecedented first meeting of a sitting U.S. president and a North Korean leader began with Trump and Kim coming together in front of a background of U.S. and North Korean flags as dozens of cameras snapped photos.

Trump’s motorcade arrived first at the Capella Hotel on Singapore’s resort island of Sentosa. Kim’s motorcade arrived a few minutes later.

The two men then sat side by side before beginning their solo talks with Trump predicting a “great discussion.”

“We’re going to be tremendously successful and it’s my honor, and we will have a terrific relationship, I have no doubt,” Trump said.

Kim said through an interpreter that it was “not easy to get here” and that “old prejudices and practices worked as obstacles on our way forward, but we overcame all of them and we are here today.”

The White House announced Monday that Trump would leave Singapore Tuesday night after meeting with Kim, adding that talks between U.S. and North Korean officials “are ongoing and have moved more quickly than expected.” 

Trump is scheduled to address the media before flying out of Singapore. Previous reports had suggested Trump would leave Wednesday.

On the eve of the first encounter between a sitting U.S. president and a leader of North Korea, American officials are maintaining that any resulting agreement must lead to an end of North Korea’s nuclear weapons and ballistic missile threats.

There will not be a repeat of “flimsy agreements” made between previous U.S. administrations and North Korea, Secretary Pompeo told reporters in Singapore on Monday.

“The ultimate objective we seek from diplomacy with North Korea has not changed — the complete, verifiable and irreversible denuclearization of the Korea Peninsula is only outcome that the United States will accept,” Pompeo said.

U.S. Secretary of State Mike Pompeo speaks during
U.S. Secretary of State Mike Pompeo speaks during a press briefing, June 11, 2018 in Singapore one day before President Donald Trump will meet with North Korean leader Kim Jong Un.

Sanctions will remain until North Korea completely and verifiably eliminates its weapons of mass destruction programs, Pompeo added.

“If diplomacy does not move in the right direction, those measures will increase,” he said.

Pompeo said he was “very optimistic” the meeting Tuesday between Trump and Kim would “have a successful outcome.”

He declined, however, to reveal any details of the preliminary discussions held Monday between U.S. and North Korean officials.

Pompeo did say the United States is “prepared to take what will be security assurances that are different, unique that America has been willing to provide previously. That’s necessary and appropriate.”

But when pressed by reporters, the secretary of state would not say whether that could include reduction of the number of or removal of U.S. troops in South Korea.

It is also unclear whether U.S. officials will raise human rights issues in meetings with the North Koreans. Ahead of his trip, President Trump said "every issue will be raised." But he did not address human rights issues when he met with Kim's top aide, Kim Yong-cho. Critics say ignoring the issue risks squandering leverage and abandoning the North's victims.

U.S. President Donald Trump flanked by Secretary o
U.S. President Donald Trump flanked by Secretary of State Mike Pompeo and White House Chief of Staff John Kelly attend a lunch with Singapore's Prime Minister Lee Hsien Loong and officials at the Istana in Singapore, June 11, 2018.

Trump attended a working lunch Monday hosted by Singapore’s prime minister, Lee Hsien Loong, at the Istana, which is the official residence of the city state’s president.

“We have a very interesting meeting in particular tomorrow, and I think things can work out very nicely,” Trump told Lee. “We appreciate your hospitality and professionalism and your friendship.”

Trump was presented with a birthday cake by his Singaporean host.  The U.S. president turns 72 on June 14.

Trump also spoke by telephone Monday with South Korean President Moon Jae-in, according to officials in Seoul who predicted that if Tuesday’s Singapore summit is a success it would be a “gift” to the entire world.
“President Moon and President Trump agreed Trump and Kim will be able to make a great achievement if the two leaders come together to find a common denominator through frank discussions,” Blue House spokesman Kim Eu-kyeom told reporters.

The spokesman said Trump told Moon he would send Pompeo to Seoul immediately after the summit to explain its outcome.

About 5,000 journalists are in Singapore for the occasion, but only a handful of American and North Korean reporters and photographers were permitted at the venue when the two leaders greeted each other.

Bill Gallo contributed to this report .