In Manila, Trump was scheduled to meet with leaders of the Association of Southeast Asian Nations (ASEAN) and other East Asian nations.
Duterte and Trump will likely talk about the North Korean threat and the overall security situation in the region, particularly the South China Sea dispute.
Beijing's sweeping claims also overlap with those of the Philippines, Malaysia, Brunei, and Taiwan.
Briefing reporters in Beijing during the China leg of Trump's Asia tour, US Secretary of State Rex Tillerson said the US view on the maritime dispute hadn't changed - that "claimants should stop construction and militarization" of disputed islands.
On Monday, the 31st ASEAN Summit and Related Summits will be officiated by Duterte at the Cultural Centre of the Philippines before the leaders gather at the Philippine International Convention Centre for a series of meetings, including the 40th anniversary of ASEAN-US Dialogue Relations.
At a joint statement with the two leaders in Beijing, Xi told Trump the Pacific Ocean was "big enough to accommodate both China and the United States".
Various sectoral groups staged a protest near the US embassy here on November 10, the second day in a row, in anticipation of the first visit by US President Donald Trump in time for the Asean summit on November 12.
Police used water canon to prevent hundreds of protesters reaching the US embassy in Manila ahead of Trump's arrival. "Stabbing. That was when I was 16 years old, just because we just looked at each other", he said.
Before his arrival, Trump had met with President Rodrigo Duterte on the sidelines of the Asia Pacific Economic Cooperation meetings in Danang, Vietnam.
In August, foreign ministers of Southeast Asia and China adopted a negotiating framework for a code of conduct in the resource-rich waterway, a move they hailed as progress but one seen by critics as a tactic to buy China time to consolidate its power.
Tensions in the contested waters have ratcheted up since 2014 as China has turned sandbars into islands, equipping them with airfields, ports and weapons systems and warned United States warships and aircraft to stay away from them. The country claims a huge swathe of the South China Sea.
"China is to work with ASEAN countries to maintain peace and stability, as well as development and prosperity in the South China Sea region", Xi Jinping said at the leaders' meeting on Sunday.
Among those who will be in Manila for the ASEAN meetings are Chinese Premier Li Keqiang, Russian Premier Dmitry Medvedev and Canadian Prime Minister Justin Trudeau.