Trump and Vietnamese President Tran Dai Quang issued a joint statement calling for the "full and effective implementation" of the declaration on the conduct of parties in the South China Sea, and for all claimants to clarify their maritime claims.
Four ASEAN members - the Philippines, Brunei, Malaysia, and Vietnam - have overlapping claims with China in the strategic waterway where about $3 billion in goods pass annually.
In August, foreign ministers of Southeast Asia and China adopted a negotiating framework for a code of conduct in the South China Sea, a move they hailed as progress but one seen by critics as a tactic to buy China time to consolidate its maritime power.
Ahead of the ASEAN summit, Duterte said at a ceremony that "the South China Sea is better left untouched, nobody can afford to go to war".
The commitment was made by Chinese Premier Li Keqiang during the 20th Asean-China summit held at the Philippine International Convention Center in Pasay City.
AMID the simmering dispute over the South China Sea, China on Monday, November 13, pledged to be a "good neighbor and friend" to the members of the Association of Southeast Asian Nations (Asean). In a meeting with Quang earlier in the day, Trump offered to serve as a mediator on the South China Sea disputes.
China in recent years has built artificial islands and increased its militarisation in the waters, drawing criticism from Washington, which argues that the United States has a national interest in freedom of navigation in sea lanes critical for world trade.
Mr Trump and Chinese president Xi Jinping spoke separately about the territorial rifts before an annual summit of South-east Asian nations that also includes the US, China and other global players.
"Of course, the claimant countries have to answer as a group or individually, and not one country can just give an instant reply because mediation involves all of the claimants and non-claimants", he pointed out.
Duterte took steps to thaw frosty relations with China after he won the presidency past year.
After the Philippines backed China's position, ASEAN agreed it would not have legal force.
China has dismissed that ruling as a "sham" and did not participate in the arbitration case that the Philippines filed during the administration of Duterte's predecessor.
"If I can help mediate or arbitrate, please let me know... They will not talk about it", Duterte said of China.
"We hope non-regional countries can respect the regional countries' efforts in maintaining the regional stability of the South China Sea, and play a constructive role in this aspect", foreign ministry spokesman Geng Shuang said at a regular press briefing in Beijing. I have done plenty of it from both sides.
The Chinese leader, however, would not back down on Beijing's territorial claim, Mr Duterte said.