"Please let me know", Trump said. "I am a very good mediator", Trump told Vietnamese President Tran Dai Quang earlier on Sunday.
Trump and Chinese President Xi Jinping spoke separately about the territorial rifts ahead of an annual summit of Southeast Asian nations that also includes the U.S., China and other global players.
Vietnam has long courted support from Washington in its dispute with China over the precious waterway where Beijing has built military installations and artificial islands.
China is claimant to swathes of ocean, extending far outside its internationally agreed 200-mile economic exclusion zone (EEZ).
Duterte revealed that Chinese President Xi Jinping signaled to him during a meeting that he wanted peace in the region, saying he does not want to "waste the lives of my countrymen for a useless war that can not be won by anyone".
The Philippines according to a consensus, will work through bilateral channels to appropriately handle maritime issues, Xinhua icited Duterte as saying. "They will not talk about it", Duterte said of China.
"You want to control the passage, or do we have free passage?"
The US conducts freedom of navigation exercises through the South China Sea.
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In the past, Duterte has repeatedly said he will raise the sea dispute at the proper time and avoided the issue when Manila hosted two regional meetings this year.
Despite unresolved issues, discussions between ASEAN and China have improved, Cayetano said. He added that the two need to "jointly uphold peace and stability" in the region.
US President Donald Trump, on his first Asian tour as president, offered to take on the role of peacemaker in the longstanding territorial issue.
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 USA warships and aircraft to stay away from them. However, several ASEAN member countries including Vietnam, the Philippines and Brunei have counterclaims.
He said that Trump and Xi had discussed ways to "prevent mishaps, misunderstandings and miscalculations" in the vital seaway. At $32 billion a year ago, it was the sixth largest with the United States, though less than a tenth the size of China's.
Since Trump took office, priorities in the region lie elsewhere, with United States focus largely on containing the North Korean threat. The US and Chinese militaries have had frequent standoffs in the area, with Beijing accusing the US of damaging China's sovereignty and security interests.
"(US) Foreign policy in Asia has had its oxygen sucked out the room", he said. The dispute centers around the Spratly and Paracel Islands. China bridled against interference by outside countries. The South China Sea will likely be a hot topic throughout the summit, as most claimants will be attending.