In general, both secretaries praised their summit, formally known as the Diplomatic and Security Dialogue, for involving higher level officials in both civilian and military posts than in the past and for laying the groundwork for greater engagement, better communication and reducing the risk of unsafe incidents going forward.
The South Korean leader earlier stressed a need to add dialogue to options for dealing with the provocative North, noting now only sanctions and pressure are available. "We must step up our efforts to help to curtail these sources of revenue".
The message, which comes as U.S. opinion toward North Korea has soured intensely over the death of United States student Otto Warmbier, stressed that the point of pressure on Pyongyang was to achieve dialogue.
Washington has 28,000 troops deployed in South Korea and a naval armada in the region.
South Korean President Moon Jae-in said on Thursday China should do more to rein in North Korea's nuclear program and he would call on President Xi Jinping to "lift all measures" against South Korean companies taken in retaliation against Seoul's decision to host a US anti-missile defense system.
North Korea's treatment of an American student who died after being released from detention in a coma was inhuman and United States patience with Pyongyang is running out, Pentagon chief Jim Mattis said Wednesday.
On Tuesday, Trump said on Twitter that China's efforts to bring a resolution to the North Korea crisis had "not worked out", adding: "At least I know China tried!" "I wish we would have a little more help with respect to North Korea, from China".More news: Cindy's remnants: Street flooding from South to Midwest
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Moon said he intends to discuss this plan with U.S. President Donald Trump and stressed several times that the American president shares his thoughts.
"This goes beyond any kind of understanding of law and order, of humanity, of responsibility toward any human being", Mattis said.
"So what you're seeing, I think, is the American people's frustration with a regime that provokes, and provokes, and provokes, and basically plays outside the rules, plays fast and loose with the truth", Mattis said. The funeral will be at Wyoming High School, his alma mater where tributes will be paid to the late Warmbier, according to reports.
China downplayed Trump's tweet, and stated in a press conference that it has played an "important and constructive role" in seeking peace on the Korean peninsula, Foreign Ministry spokesman Geng Shuang told reporters in Beijing. Such measures have been in place since Seoul agreed to host the THAAD U.S. missile defense system.
Secretary of Defense James Mattis reinforced the message, calling the dialogue "open and frank", and insisting, "China continues to work these issues".
Trump has made halting the North Korean nuclear threat his number one foreign policy priority.
Moon also proposed a two-stage denuclearization approach involving a "nuclear freeze" first to halt further North Korean nuclear and missile advancements, followed by termination of the North's nuclear program.