North Korea's state-run Korean Central News Agency said the two leaders agreed to the principle of "step-by-step" process and Trump expressed his intention to lift sanctions "over a period of goodwill dialogue" between the two countries.
Mr Trump's surprise promise to call off military exercises, describing them as expensive and "provocative", delighted North Korea and China but caught key United States allies off-guard.
In the poll, Trump received a 51 percent approval rating for his handling of North Korea and also led the list of leaders who should take the most credit for the summit and the joint pledge.
A task force has been also launched to prepare for possible tour programmes in the North by South Korean tourists, according to the Korea Tourism Organisation.
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Mr Pompeo was speaking at a press conference in Seoul with his South Korean and Japanese counterparts.
"The world should rest assured the United States, Republic of Korea and Japan remain committed to achieve complete, verifiable and irreversible denuclearization of North Korea", he said.
THE FACTS: Trump is wrong to suggest North Korea no longer poses a nuclear threat.
Kim wants American troops to withdraw from the Korean peninsula; Trump has indicated a readiness to draw down the 27,000 personnel stationed in South Korea and has made it clear that he would prefer to withdraw all troops from that country.
Illustrative: US Army M1-A2 tanks fire during US-South Korea joint military live-fire drills at Seungjin Fire Training Field in Pocheon, South Korea, near the border with North Korea, April 26, 2017.
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A White House read-out of Trump's meetings with Prime Minister Lee Hsien Loong today did not include mention of a state visit. She said their belief is that it occurred "because South Korea attacked them, which is not true". "Now we have this meeting".
Pompeo had told reporters on Wednesday that the North Korean nuclear disarmament could take two years to complete. That kind of thing is very threatening to North Korea.
The likelihood of Kim Jong Un launching a first strike against the USA, thereby bringing on "fire and fury", was low.
China, one of the earliest allies of the hermit state, also had a "win-win situation" in the recently concluded summit, said Cabalza, noting that Kim first met with Chinese President Xi Jinping in March.
Freezing the regular military exercises with South Korea is a major concession to North Korea that has long claimed the drills were invasion preparations. "And the sanctions relief can not take place until such time as we have demonstrated that North Korea has been completely denuclearized". Gen. Kim Do-gyun told reporters before the talks. Here is the essence of the statement: "The United States and the DPRK commit to hold follow-on negotiations". Regarding the alliance, we are dealing with all the issues under the premise that we maintain the ironclad joint defense posture.
President Trump described his meeting with Kim as a resounding success and in a tweet said, "There is no longer a nuclear threat from North Korea". USA officials said it was unclear what types of training involving US and South Korean troops might cross into Trump's now forbidden zone of "war games".
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"China opts for the first one and has made such a decision, we hope the USA will make a wise choice and China on its part is prepared on all fronts", remarked Wang.