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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 Korean state media reported the election of the South's new left-leaning president Moon Jae-In after a two-day delay, but at unusual length.
It added the two leaders "agreed to continue to strengthen the United States-Republic of Korea alliance and to deepen the enduring friendship between our two countries".
A big challenge will be U.S. President Donald Trump, who has proven himself unconventional in his approach to North Korea, swinging between intense pressure and threats and offers to talk.
China hopes South Korea's government attaches importance to its concerns and takes real steps to promote the healthy and stable development of ties, Xi said.
One of the hot topics of discussion could be North Korean President, Kim Jong Un and possible threat from his nuclear weapons program.
"In current circumstances where there is growing uncertainty on the Korean peninsula and the region, the U.S". Modi invited the South Korean President to India, also expressing hope to hold bilateral talks at upcoming global meetings like G20 summit slated for July. They discussed a range of nuclear, security and bilateral issues, according to a person familiar with the talks.
Korea Economic Institute analyst Troy Stangarone told VOA that Moon has stated he would only negotiate with North Korea after consulting with the United States.
The State Department would only say such meetings "are routinely held on a variety of topics around the world and occur independent of US government involvement".
Numerous missile tests were considered failures, but experts have said Pyongyang is making faster-than-expected progress toward its stated goal of developing a nuclear-tipped missile that could reach the US mainland. "I will leave the Blue House and begin the age of a "Gwanghwamun president" as soon as preparations are done", the new president said in his first speech on Wednesday. He has said he would be prepared to go to Pyongyang "if the conditions are right".
The election of Moon, who has criticized the deployment of the defense system, could offer a chance to reset relations. China retaliated against the decision to allow the system by suspending Korean retail giant Lotte Mart's stores in its territory, banning package tours and imposing stricter rules for sales of Korean cosmetics products.