At the start of his meeting with Vietnam's president Tran Dai Quang, he said he was prepared to act as mediator between claimants to the South China Sea, which include Vietnam and China.
Vietnam, the Philippines, Malaysia, Brunei and Taiwan also have claims in the sea, and the dispute has always been seen as a potential trigger for conflict in Asia. "Unbridled, undisturbed, unmolested while we use that small way from the Indian Ocean. facing Palawan", Duterte said, referencing the southern Philippines province which juts out into the South China Sea.
"I'm a very good mediator and arbitrator", he said.
Following the conclusion of the APEC meetings, many attendees will next head to Manila, where a meeting of members of the Association of Southeast Asian Nations (ASEAN) will commence.
"China will continue to work with ASEAN countries to safeguard peace, stability and prosperity of the South China Sea region", China's official Xinhua news agency cited Xi as saying to Duterte.
The resource-rich disputed waters of the South China Sea have always been a bone of contention between the regional players - China, Taiwan, Vietnam, Philippines, Indonesia, Malaysia, and Brunei.
Kelly, Trump's chief of staff, said human rights would be a "hot topic" in the Philippines but declined to make definitive statements about Duterte's possible role in abuses-or whether reports of abuses were true.
China insists that the territorial issues should be handled directly between countries in the region.
When he raised concerns over China's increasing military capability in the South China Sea, Duterte said Xi replied, "No, it's nothing".
The United States has criticized China's construction of islands and its build-up of military facilities in the sea, and is concerned they could be used to restrict free nautical movement.
He said that Trump and Xi had discussed ways to "prevent mishaps, misunderstandings and miscalculations" in the vital seaway.
In recent days, North Korean state-run media has taken to referring to Mr Trump's age.
While China is frustrated with the intractable nuclear standoff, the U.S. focus on it does afford China "a lot of strategic opportunities", Harry Kazianis, director of Defense Studies at the Center for the National Interest told CNN ahead of Trump's Asia trip.
China and Vietnam have been in dispute over Chinese island building in the South China Sea, and Vietnam's sudden halt to gas exploration in July after a Chinese threat. The South China Sea will likely be a hot topic throughout the summit, as most claimants will be attending.
An global tribunal has also ruled against China's maritime claims but Beijing has refused to recognize the court's ruling.