North Korean leader Kim Jong Un pledged to work toward the "complete" denuclearization of the Korean Peninsula while U.S. President Donald Trump committed to provide security guarantees to Pyongyang in the first-ever summit between their two countries Tuesday.

Speaking at a signing ceremony for a joint statement issued at the conclusion of historic summit in Singapore, Trump called the document "pretty comprehensive" and said the two sides will start the process of ridding the North of nuclear weapons "very quickly."

(Kevin Lim/THE STRAITS TIMES/Handout)

However, he acknowledged that it takes "a long time to pull off complete denuclearization...scientifically."

Some question the effectiveness of the statement because it makes no reference to concrete measures nor to a timeframe to achieve denuclearization. It does not say how Trump will provide security assurances to Pyongyang, either.

Speaking in a post-summit news conference that stretched over an hour, Trump said sanctions on North Korea will remain in effect "in the meantime" to compel the country to take credible actions toward denuclearization.

But in what appeared to be part of confidence-building measures, Trump said the United States will suspend joint military exercises with South Korea as long as dialogue continues with Pyongyang, amounting to a major concession to the North.

Full text of Trump-Kim joint statement

"We'll be saving a tremendous amount of money. Plus, I think it's very provocative" for North Korea, he said.

Trump said he is not considering reducing U.S. troop levels in South Korea, but did not rule out the possibility of doing so in the future.

The president quoted Kim as saying North Korea will soon destroy a major missile engine testing site. Trump hailed the move as "a big thing."

Trump said he raised the issue of the North's abductions of Japanese nationals in the 1970s and 1980s, but did not elaborate, only saying, "They're going to be working on that."

The statement does not address the abduction issue, nor short- and medium-range missiles capable of hitting South Korea and Japan.

According to the statement, U.S. Secretary of State Mike Pompeo and "relevant high-level" North officials will hold follow-up negotiations "at the earliest possible date" to implement the outcomes of the Trump-Kim summit.

The statement, however, does not mention "complete, verifiable and irreversible denuclearization," a concept Pompeo has said would be the only outcome the United States will accept.

Trump insisted that a denuclearization process be verified by exerts from the United States, the International Atomic Energy Agency and other parties.

Trump expressed eagerness to continue engagement with Kim, saying he will visit Pyongyang at an appropriate time and he has invited the North's leader to the White House.

Following their first handshake around 9 a.m. in a reception area of Capella Singapore, a luxury hotel on the resort island of Sentosa, the leaders had a one-on-one meeting accompanied only by their interpreters, before attending an expanded meeting with senior officials of both sides and a working lunch.

Asked by reporters between the one-on-one and expanded sessions if he would give up the North's nuclear weapons, Kim made no reply.

Western, Korean dishes served at lunch for Trump-Kim summit

IN PICTURES: Chronology of major events leading to 1st U.S.-N Korea summit

GALLERY: Scenes of Pyongyang

Speaking at the signing ceremony, Kim said, "We had a historic meeting and decided to leave the past behind...The world will see a major change."

The two countries also committed to recovering the remains of prisoners of war and those missing in action during the Korean War, including the immediate repatriation of those already identified, according to the statement.

"While the armistice was agreed to, the war never ended, to this day never ended," Trump said. "But now we can all have hope that it will soon end."

The 1950-1953 war halted by an armistice, not a peace treaty. The armistice -- signed by the U.S.-led United Nations Command, North Korea and Chinese People's Volunteer Army -- has left the main combatants technically in a state of war.

In a prelude to the summit, Kim and South Korean President Moon Jae In, meeting in the truce village of Panmunjeom on April 27, expressed their commitment to the "complete" denuclearization of the peninsula and agreed to declare an end to the Korean War by the end of the year.

(Kevin Lim/THE STRAITS TIMES/Handout)