Both Mr Moon and Mr Xi agreed that denuclearising North Korea was a "common goal".
"President Trump said he looks forward to working with President Moon and invited him to visit Washington at an early date".
Both the US and South Korea are keen on dismantling the nuclear program of Kim Jong Un and hence, are open to maintaining the sanctions on North Korea already laid in place by Trump's administration.
Nonetheless, aside from wanting to restore normal relations and trade with North Korea, Moon wants to have the same with China.
Moon said he planned to send a special envoy to Russian Federation in the near future.
Moon is a liberal who advocates a more conciliatory approach to North Korea compared with his conservative predecessor.
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Xi congratulated Moon on his election and the leaders agreed to exchange special envoys as soon as possible, Yoon said.
The North's state-run propaganda Web site Uriminzokkiri claimed that North Korea policies that are hostile to fellow countrymen and intensify confrontation should be fundamentally eliminated.
According to Zhao, China's understanding on how to deal with North Korea is very much in line with the new South Korean president.
Not only does he need to reach out to Pyongyang but he should also act to ensure that Seoul is in control of its foreign policy.
Park was South Korea's 11th president who was impeached making Moon take the seat with his landslide victory in South Korea election. The talks involve both South and North Korea, Russia, the United States, Japan and China.
Trump has also been calling for a renegotiation of the bilateral free trade agreement (FTA) and for Seoul to shoulder a larger cost of maintaining USA troops in Korea and pay for a $1 billion antimissile system.
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China has invited South Korea to a summit on a global trade initiative in Beijing in what appears to be the latest move to fix a strained relationship and reach out to the new South Korean president.
But Abe also said "dialogue for dialogue's sake would be meaningless" and he called on North Korea to demonstrate "sincere and concrete action", Hagiuda said, adding that Moon shared Abe's views. That could slow any attempt at rapprochement with the North's unpredictable leader, Kim Jong Un, at a time of broad global support for sanctions.
The delegation will also include two other ruling party lawmakers, Vice Foreign Minister Lim Sung-nam and a high-level official from the finance ministry, the Ministry of Foreign Affairs said.
"In South Korea, what defines you as a conservative or progressive candidate comes down to your policy position on foreign policy", James Kim, an worldwide relations expert at the Asan Institute for Policy Studies in Seoul, told Sputnik.
A phone conversation between Moon and US President Donald Trump on Wednesday night also touched on the Korean Peninsula.
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