Japanese Prime Minister Shinzo Abe and Mr Xi have also agreed to deepen cooperation between the two countries on North Korea, Abe said on Saturday after meeting Mr Xi.
At the meeting, the two countries agreed to deepen their cooperation on North Korea and to hold a trilateral summit with South Korea at the earliest possible date.
On the Korean Peninsula situation, Xi told Moon that China sincerely hopes for the best for the peninsula, and encourages South Korea to resume contact and dialogue with the Democratic People's Republic of Korea and restart cooperation for reconciliation.
On the Thaad issue, Xi emphasized that the October 31 agreement between the two countries marked a "new start and a good beginning".
"At the end of the meeting, President Xi said this is a meeting that marks a fresh start of relations between Japan and China". Xi stressed that the two nations should respect each other regarding their key interests and critical issues, establish political mutual trust and enhance bilateral communication and cooperation.
As part of a broader effort to boost the tourism industry, the government said Friday it will temporarily allow tourists from three Southeast Asian countries - Indonesia, Vietnam and the Philippines - to enter the country without a visa.
Restoring relations between Korea and China, getting North Korea to participate in the PyeongChang Olympics and creating an atmosphere conducive to talks with Pyongyang about denuclearization is a part of Moon's comprehensive strategy toward the North, outlined in his Berlin address in July.
Moon's visit to Indonesia is his first to Southeast Asia since taking office.
The Blue House initially said the Thaad issue was not going to be raised during the summit, but Xi brought it up.
President Moon attends a meeting of the APEC Business Advisory Council at the Furama Resort Hotel in Da Nang, Vietnam on November 10.
The report said the Chinese president also remarketed that China-South Korea relations are at a critical point.