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.
Moon responded by saying the Philippines is "very special" to South Korea.
Japan, China and South Korea are now in talks with ASEAN on the Regional Comprehensive Economic Partnership, another pan-Asian trade deal.
The East Asia Summit meeting was scheduled to issue a chairman's statement on Tuesday that condemns North Korea, a nation that continues to develop nuclear weapons and missiles, according to a draft obtained by The Yomiuri Shimbun.
The South Korean president arrived here on Sunday as part of his three-nation trip that earlier took him to Indonesia and Vietnam.
Still, Moon said anything could be discussed if the North comes to the dialogue table.
Moon, however, insisted now was still time to focus on keeping maximum pressure and sanctions against the impoverished North. Meanwhile, the two agreed for Moon to visit Xi in China in December to hold another round of summit talks, while Moon invited Xi to South Korea during the Pyeongchang Winter Olympic Games, which falls in February next year, the spokesman said.
They also agreed to accelerate ongoing negotiations between South Korea and the Eurasian Economic Union for a free trade agreement. "After confirming that position, President Xi said that it is nevertheless important at the present moment to work on the future-oriented development of the two countries" relations".
'World's oldest wine' found in 8000-year-old jars in Georgia
One of the most important crafts was pottery, which enabled the fermentation and storage of wine. So it seems like we have the Neolithic Georgians to thank for Chardonnay and Merlot.
The South Korean president is now on an eight-day trip to Southeast Asia that also included his participation in the annual Asia-Pacific Economic Cooperation Economic Leaders' Meeting in Danang, Vietnam, as well as a number of bilateral talks with other global leaders, including Chinese President Xi Jinping and Chinese Prime Minister Li Keqiang.
Following the roughly 50-minute long bilateral the Blue House said there was an air of determination to push the relationship forward at the sideline summit talks in Danang.
Still, Moon's planned visit to China coincides with an improvement in relations after the nations agreed to put aside a dispute over the deployment of a US missile shield on South Korean soil.
The South Korean leader noted the THAAD issue may not have completely gone away, but insisted the countries have clearly left it behind.
The two countries agreed to normalize their ties in a joint statement issued by their foreign ministries on October 31.
The Chinese prime minister said the countries' relations will continue to improve, though it may take time.
He said differences in understanding between South Korea and China, North Korea's lone major ally, regarding the deployment of the U.S. Terminal High Altitude Area Defence (THAAD) system on South Koran soil had not been resolved. Since he took office past year, he has pivoted toward China.