While South Korea, China and Japan all worry about North Korea, ties between South Korea and China have been strained by South Korea's decision to install a United States anti-missile system in defence against the North.
Mr Moon favours engagement with Pyongyang to bring it to the negotiating table, unlike his conservative predecessors and the US Trump administration, which backs stronger sanctions and has threatened military action.
South Korea's new president launched worldwide efforts to defuse tensions over North Korea's weapons development yesterday, urging both dialogue and sanctions while also aiming to ease Chinese anger about an American anti-missile system.
That said, it is not clear that Seoul and Beijing can immediately get on the same page and put bad blood behind them.
"I would like to use this opportunity to wish to the new president of the Republic of Korea Mr. Moon Jae-in and the Korean people a new and successful start and to invite him to be the first Korean president to visit Israel", he said.
"The new South Korean government will actively communicate with China on these issues and seek appropriate resolutions", the statement quoted Moon as saying.
The deployment of THAAD was agreed past year by South Korea's previous administration after North Korea conducted a long-range rocket launch that put an object into space. Moon said he would send a special envoy to Russian Federation soon and Putin said he would welcome the envoy.
Yoon said the initiative was mentioned during a 40-minute phone call yesterday, the first between Moon and China's President Xi Jinping. "The U.S. -South Korea alliance is the foundation of our foreign policy, and will continue to be so".
Leaders of 29 countries and senior officials from many more gather in Beijing on Sunday for to discuss Xi's initiative to expand trade links between Asia, Africa and Europe through billions of dollars in infrastructure investment.
South Korea and the United States began deploying the THAAD system in March and it has since become operational.
"While supporting South Korea's position and opposing North Korea's nuclear development, President Moon explained his own policy of employing both sanctions and dialogue at the same time to help resolve the North Korean nuclear issue", Yoon said.
The deployment is also unpopular among South Koreans who live near the site that hosts the system because they believe it makes them a target.