Both Moon and Xi agreed that denuclearising North Korea was a "common goal". A progressive leader, Moon favours dialogue and has strongly opposed Seoul's hawkish policies towards North Korea over the past decade.
Last month, the state-run newspaper Rodong Sinmun claimed US-Australian military exercises in northern Australia were preparation for nuclear war against North Korea and threatened Darwin with a potential retaliatory strike. His appointment requires parliamentary approval.
China and South Korea enjoyed an increasingly warm relationship early in the tenure of Moon's predecessor Park Geun-hye, drawn together by shared historical differences with Japan.
North Korea argued that there would be no need for Washington to "beg or threaten" countries to implement the measures if the sanctions had a clear legal basis.
Ahead of the election, Johns Hopkins University lecturer Eunjung Lim cast predictions in the online publication The Conversation about what challenges the new leader of South Korea-an essential US ally-might face.
China says the system does little to curb the threat posed by North Korea's nuclear and missile programmes, which Pyongyang has been pressing ahead with in defiance of USA pressure and United Nations sanctions.
North Korea is threatening US citizens detained in its country, saying it has the right to "ruthlessly punish" them. Their divergent approaches to Pyongyang could sour relations between the USA and South Korea.
North Korea is now hung up on a narrative that the CIA and South Korea's National Intelligence Service (NIS) hired a North Korean lumberjack working in Russian Federation to detonate a biochemical weapon during a military parade to end the life of the young North Korean dictator Kim Jong Un.
"U.S. citizens in the Democratic People's Republic of Korea are at serious risk of arrest and long-term detention under North Korea's system of law enforcement", the officials said.
Abe said he looked forward to working with Moon to improve relations, describing South Korea as one of Japan's most important neighbours.
There's widespread opposition in South Korea to the THAAD deployment and loud protests from China, which also sees the system as a security threat. National Security Advisor H.R. McMaster, for example, reassured Korea that Trump really wasn't going to make them pay for THAAD.
Moon has said the decision was made hastily and his government should have the final say, but analysts say it would be hard to remove THAAD now it has been deployed.
A Downing Street spokesman said the two leaders vowed to remain "close partners" on issues including defence and security.
Pyongyang has said a North Korean citizen named only as Kim was bribed and blackmailed to carry out the attack. The American participants typically report their observations to the United States administration.