Moon accepted the invitation at an "early date" but no specific time was set, according to a statement. After Park was impeached and jailed, Moon, a leftist former human rights lawyer who lost to her in the last presidential election, was the obvious alternative.
"Sanctions against North Korea are also a means to bring the North to the negotiating table aimed at eliminating its nuclear weapons", Yoon told a briefing, adding that Xi indicated his agreement.
In response, Moon said he would like to exercise wisdom to resolve various issues so the two East Asian neighbors can develop a good relationship.
On Tuesday, Beijing confirmed that official delegation from Pyongyang would also attend the summit. China has vigorously opposed the deployment of a US anti-missile system in South Korea, saying it threatens Chinese security and will do nothing to resolve tensions with North Korea.
The missile defence system's deployment has hit tourism hard, with visitor inflow from China plunging 40 per cent in March from a year ago to 360,782, the Korea Tourism Organisation said.
The six-party talks on ending North Korea's nuclear ambitions have been stalled since late 2008, largely due to a North Korean boycott.
The two sides agreed on the importance of denuclearizing the peninsula.
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Moon also spoke to Xi about the difficulties faced by some South Korean companies doing business in China facing discrimination in retaliation for the THAAD deployment.
Stangarone also added that whatever global plans Moon has, the economic situation in South Korea and the fact that he was elected following an impeachment mean that domestic issues will constrain what he wants to do.
A South Korean presidential spokesman said that the Chinese leader - who initiated the call - "explained the reasons for Beijing's strong and repeated opposition" to the deployment, Yonhap news agency reported.
Moon's victory has been characterized as a setback in U.S. She is now in prison awaiting trial on corruption charges.
South Korea says it needs Thaad to defend itself from North Korea, but China believes its radars threaten regional security.
"How to respond to North Korea.is an urgent issue". The industrial park was shut down by the South Korean government in February 2016, in response to a ballistic missile test by North Korea.
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 USA mainland.