Moon responded by saying the Philippines is "very special" to South Korea.
Moon's suggestion of forming a regional community came at an annual summit with the Association of Southeast Asian Nations, known as the ASEAN Plus Three.
Xi said China was willing to work with South Korea to improve bilateral ties, but called on Seoul to make responsible decisions about THAAD.
The growing threat of North Korea's nuclear development in the region is also the leaders' agenda.
In their opening remarks during the 20th ASEAN Plus Three (APT) Summit, Chinese Premier Li Keqiang, Japanese Prime Minister Shinzo Abe, and South Korean President Moon Jae-In noted the challenges protectionism as an economic policy had posed to their respective countries.
The South Korean president arrived here on Sunday as part of his three-nation trip that earlier took him to Indonesia and Vietnam.
On Friday, the North said it did not oppose dialogue, but would "never put the issue related to the supreme interests of the DPRK and security of its people on the bargaining table".
Moon, however, insisted now was still time to focus on keeping maximum pressure and sanctions against the impoverished North.
"And I hope that we could make joint efforts to further strengthen this trend".
Pyongyang remains silent despite repeated invitations from the South Korean president to take part in the Olympic Games to be held February 9-25.
They also agreed to accelerate ongoing negotiations between South Korea and the Eurasian Economic Union for a free trade agreement.
Meeting for the first time since their modus vivendi to put aside their differences and end a year-long standoff over the deployment of a US missile defense system in South Korea, Presidents Moon and Xi reaffirmed their joint resolve to mend ties and restore cooperation in all areas. "I believe we have created a chance to quickly normalize the countries' relationship through my talks with President Xi Jinping". Speaking from the Asia-Pacific Economic Cooperation summit in Vietnam on Saturday, Kang Kyung-wha said two months without any nuclear tests from the North was a good sign, reports Bloomberg.
Moon insisted his summit with Xi, held on the sidelines of the APEC summit in Danang, marked a fresh start in the countries' bilateral relations. "They do not deviate from the scope of the joint statement on THAAD issued on October 31", said a senior the official, who was present during the summit.
Lian Degui, a professor with the School of Japanese Studies at Shanghai International Studies University, said Trump's visits to China, Japan and South Korea sent a signal that the USA needed cooperation among the three countries to tackle the North Korean nuclear issue.
Highlighting the apparent end of the months-long dispute, Moon has agreed to visit China next month for what will be his third bilateral summit with the Chinese leader since taking office in May.