But the current North Korean leader, Kim Jong Un, has never met Chinese President Xi Jinping, nor has he ever visited Beijing, and relations between the two allies - said to have been "forged in blood" after the Korean War - are at their worst point in years.
Before leaving for Beijing, Lee told reporters that summit talks between Moon and Chinese President Xi Jinping could take place on the sidelines of a Group of 20 meeting to be held in Germany in July and then again in time for August 24 when both countries mark the 25th anniversary of building diplomatic ties.
"We are living in the reality where there is a high possibility of military clashes" along the disputed sea border off the Koreas' west coast or along the heavily-fortified land frontier that divides them, he said. It's controlled by a family-based dictatorship, now represented by 34-year-old Kim Jong-un.
Haley said the worldwide community wants to be able to support North Korea, but as long as it continues trying to grow its nuclear programme with missile tests, North Korea would remain an "island".
"I want to confirm that we are categorically against the expansion of the club of nuclear powers, including with the Korean peninsula and North Korea", said Putin, who said any such move would be "harmful and unsafe".
South Korea wants to reopen communications with North Korea, officials said yesterday. "But from past year, the South Korea-China relationship suffered a setback which should not have happened, and this is an unwanted situation".
North Korea has been "a flagrant menace for far too long", the statement said. The United States is not past looking at third-country entities who are helping North Korea, and putting sanctions against them.
"The state of the alliance is strong and I am fully confident that it will only grow stronger between our two administrations", Pottinger said.
Trump has long touted his plan to pressure China to do more to rein in North Korea.
However, since Kim considers his possession of nuclear weapons a key element that ensures his continued power, his adversaries, including China's Xi, obviously confront a challenge in reaching an agreement.
US Ambassador Nikki Haley said the United States was working with China, the North's main ally, on a new sanctions resolution and warned that all countries must step up action against North Korea or face measures themselves.
The pair told the AP that if the North ultimately thought it was under immediate attack or threatened, one possible scenario would be that it would first target the South Korean city of Busan, which is often used as a port by the US Navy.
State media paraphrased North Korea's leader as saying that "the most ideal weapon systems in the world will never become the eternal exclusive property of the US", warning that "the USA should not. disregard or misjudge the reality that its mainland and Pacific operation region are in (North Korea's) sighting range for strike". "He said, however, that what he's willing to do is not talk for talk's sake but for talks that produce an outcome", the envoy said. North Korea has also launched satellites into orbit on long-range rockets that share some of the same technology as missiles.
However, experts say these pro-engagement policies are not likely to happen anytime soon, especially with the North's latest missile test on Sunday.
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