Trump is expected to try during the summit to shore up relations, which have been strained by the mercurial Duterte's notorious anti-US sentiment and his enthusiasm for better ties with Russian Federation and China.
"If I can help mediate or arbitrate, please let me know ..."
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.
Speaking in Vietnam, Trump said he was "a very good mediator and arbitrator" and could help to make progress on the regional dispute, in which five countries contest China's sweeping claims to the waters.
From Vietnam, Trump flies to the Philippines for a meeting with ASEAN leaders before he heads back to Washington.
The South China Sea dispute will be one of the major issues at the East Asia Summit in The Philippines this week.
Mr Trump's offer comes ahead of Chinese president Xi Jinping's attempt to woo Vietnam on the issue in a state visit.
Leaders of Southeast Asian countries and China agreed Monday to begin negotiations on a "code of conduct" aimed at controlling aggressive actions in the disputed South China Sea, a step they described as a milestone, but some experts said was unlikely to ensure compliance.
Nearly all of the South China Sea, one of the world's busiest waterways, is claimed by China.
Xinhua news agency reported that the Chinese and Vietnamese sides "reached an important consensus in accordance with leaders of the two parties and countries, to appropriately manage maritime issues, steadily advance all forms of maritime cooperation including joint development and jointly strive to uphold peace and stability in the South China Sea".
"Meanwhile, we hope the countries outside the region will respect regional countries' efforts in safeguarding peace and stability in the South China Sea and constructively contribute to that", Geng said.
He said that Trump and Xi had discussed ways to "prevent mishaps, misunderstandings and miscalculations" in the vital seaway.
Leaders from China, the United States. and seven other nations are joining ASEAN at their annual summit.
The disputes are expected to get the spotlight at the summit, along with the North Korean nuclear threat and terrorism.
"(US) Foreign policy in Asia has had its oxygen sucked out the room", he said.
India has been supporting freedom of navigation and access to resources in the South China Sea in accordance with principles of worldwide law, including the 1982 UN Convention on the Law of the Sea. "For China, this is their time".
It's claims are based on its traditional "nine-dash line" - waters that extend hundreds of miles to the south and east of its island province of Hainan, abut its neighbors' claims and, in some cases, encroach upon them.
An worldwide tribunal has also ruled against China's maritime claims but Beijing has refused to recognize the court's ruling.