The EU has praised the summit between US President Donald Trump and North Korean leader Kim Jong-un as a "crucial and necessary step", saying it indicated "complete denuclearisation" of the Korean peninsula could be achieved.
Trump said he would meet Kim "many times" and US Secretary of State Mike Pompeo could meet North Korean officials as early as next week.
The two leaders signed a vague four-point statement in which North Korea reaffirmed its commitment to work toward "complete denuclearization" but the promise came without a timetable or mention of any verification of the North's progress.
Moon played a mediator role between Kim and Trump, having already held two summits with Kim in April and May.
Israeli Prime Minister Netanyahu drew analogies to the Iran nuclear deal, noting that those who support Trump's pledge to de-nuclearize North Korea should be supportive as well of the president's efforts to ensure that Iran never has the capacity to produce nuclear arms.
"The drills and the USA military stationed in South Korea play a vital role in East Asia's security", Japan's Defence Minister Itsunori Onodera said when asked about Mr Trump's surprise announcement.
The report added Trump said he "understood" and promised to halt joint U.S. "Until such time as North Korea can take those concrete steps to denuclearize, our policy should be to continue the maximum pressure campaign", Gardner said.
"I think the fact that Donald Trump showed some strength and showed some backbone has brought Mr. Kim Jong Un to the negotiating table", Lamborn said. The talks are expected to focus on denuclearization of the Korean Peninsula.
"We would like to seek an understanding of this between Japan, the US and South Korea", Japan's defence minister, Itsunori Onodera, said.
Asked about Trump's comments, South Korean presidential spokesman Kim Eui-kyeom told reporters there was a need to seek measures that would help improve engagement with North Korea but it was also necessary to confirm exactly what Trump had meant.
Pyongyang has reason to feel confident after the meeting, where Kim stood as an equal with Trump in front of their nations' flags. "The objective of those exercises is to maintain the readiness of South Korean and United States forces to defend South Korea if necessary; they are a permanent necessity to maintain deterrence, not a bargaining chip".
Despite the lack of detail in the summit agreement, Trump stressed at a news conference afterward that he trusted Kim to follow through.
The administration's argument is that the incremental approach used by past administrations has allowed North Korea to extract rewards and incentives from the USA, only to ultimately renege and refuse to give up its nukes.