Tough sanctions will remain on North Korea until its complete denuclearization, the U.S. secretary of state said on Thursday.

North Korean state media reported on Wednesday Kim and Trump had recognized the principle of "step-by-step and simultaneous action" to achieve peace and denuclearization on the Korean peninsula.

President Donald Trump and Kim Jong Un's summit statement provided no details on when Pyongyang would give up its nuclear weapons program or how the dismantling might be verified.

SEOUL (Reuters) - Tough sanctions will remain on North Korea until its complete denuclearization, the U.S. secretary of state said on Thursday, apparently contradicting the North's view that the process agreed at this week's summit would be phased and reciprocal.

U.S. President Donald Trump and North Korean leader Kim Jong Un issued a joint statement after their Singapore meeting that reaffirmed the North's commitment to "work toward complete denuclearization of the Korean Peninsula", an end to joint U.S.-South Korean military exercises and gave U.S. guarantees of security to North Korea.

"President Trump has been incredibly clear about the sequencing of denuclearization and relief from the sanctions," Secretary of State Mike Pompeo told reporters after meeting South Korea's president and Japan's foreign minister in Seoul.

"We are going to get complete denuclearization; only then will there be relief from the sanctions," he said.

North Korean state media reported on Wednesday Kim and Trump had recognized the principle of "step-by-step and simultaneous action" to achieve peace and denuclearization on the Korean peninsula.

The summit statement provided no details on when Pyongyang would give up its nuclear weapons program or how the dismantling might be verified.

Skeptics of how much the meeting achieved pointed to the North Korean leadership's long-held view that nuclear weapons are a bulwark against what it fears are U.S. plans to overthrow it and unite the Korean peninsula.

However, South Korean President Moon Jae-In said the world, through the summit, had escaped the threat of war, echoing Trump's upbeat assessment of his meeting with Kim.

"There have been many analyses on the outcome of the summit but I think what's most important was that the people of the world, including those in the United States, Japan and Koreans, have all been able to escape the threat of war, nuclear weapons and missiles," Moon told Pompeo.

Pompeo insisted Pyongyang was committed to giving up its nuclear arsenal but said it would "be a process, not an easy one".

Kim Jong Un understood getting rid of his nuclear arsenal needed to be done quickly and there would only be relief from stringent U.N. sanctions on North Korea after its "complete denuclearization", Pompeo said.

"Everybody much safer"

North Korea's Hwasong-15 intercontinental ballistic missile, or ICBM, before a test launch in November 2017. KCNA

The United States has long insisted on complete, verifiable and irreversible denuclearization by North Korea but, in the summit statement, North Korea committed only to the "complete denuclearization of the Korean Peninsula", phrasing it has used in the past.

Trump returned to the United States on Wednesday and took to Twitter to hail the meeting, the first between a sitting U.S. president and a North Korean leader, as a major win for American security.

"Everybody can now feel much safer than the day I took office," Trump tweeted. "There is no longer a nuclear threat from North Korea. Meeting with Kim Jong Un was an interesting and very positive experience. North Korea has great potential for the future!"

Democratic critics in the United States said the agreement was short on detail and the Republican president had made too many concessions to Kim, whose country is under U.N. sanctions for its nuclear and weapons programs and is widely condemned for human rights abuses.

Pompeo said Trump's comments about the reduced threat from North Korea were made "with eyes wide open".

"It could be the case that our effort won’t ... work but we are determined to set the conditions so that we can right this failure of decades and reset the conditions for North Korea's participation in the community of nations," Pompeo said after a trilateral meeting with South Korean Foreign Minister Kang Kyung-wha and Japanese Foreign Minister Taro Kono.

Maintain readiness

South Korean Army K1A1 and U.S. Army M1A2 tanks fire live rounds during a U.S.-South Korea joint live-fire military exercise, at a training field, near the demilitarized zone, separating the two Koreas in Pocheon, South Korea April 21, 2017. REUTERS/Kim Hong-Ji/File Photo

Tokyo has reacted with concern at Trump's plans to cancel military exercises with South Korea, saying such drills are vital for East Asian security.

Two North Korean missiles flew over Japan last year as Pyongyang made rapid advances in its program to develop a missile capable of striking the U.S. mainland with a nuclear warhead.

Tokyo is working on arranging a meeting between Prime Minister Shinzo Abe and Kim Jong Un, with one possibility including the premier's visit to Pyongyang around August, the Yomiuri newspaper reported.

A government source familiar with the matter told Reuters that Japanese officials planned to discuss the summit with North Korean officials at an international conference on Northeast Asian security to be held in Mongolia on Thursday and Friday.

Kang said South Korea and the United States shared the same goals and approach to achieving denuclearization.

"The issue of South Korea-U.S. joint exercises is one that should be discussed between the military authorities between the two Koreas, and it will be going forward," Kang said. "But the issues of the alliance should be dealt with under the premise we maintain joint ironclad defense posture."

The U.S. intelligence assessment of the nuclear and other military threat posed by North Korea to U.S. and allied forces in Asia and the northwest Pacific remained unchanged despite Trump and Moon's assertions about the North Korean nuclear threat being over, a senior U.S. official responsible for studying the North Korean military said.

U.S. officials said it was unclear what types of training involving U.S. and South Korean troops might cross into Trump's now forbidden zone of "war games". But big, joint U.S.-South Korean exercises appeared off-limits under the new guidance.

"Make no mistake, we are going to maintain the readiness of our forces in South Korea," said one U.S. official, speaking on condition of anonymity. The official acknowledged, however, it was still not certain how that was going to happen.

The United States maintains about 28,500 soldiers in South Korea, which remains in a technical state of war with the North after the 1950-53 Korean War ended in a truce rather than a peace treaty.