The two leaders held bilateral talks at the Crowne Plaza hotel at the end of the Asia Pacific Economic Cooperation (APEC) summit in Da Nang, Vietnam.
U.S. President Donald Trump, author of the bestseller "Art of the Deal", offered his assistance in the dispute over China's sweeping claims in the South China Sea. "I want to solve North Korea, Syria, Ukraine, terrorism, and Russian Federation can greatly help!"
He acknowledged China's position on the South China Sea, and said he knew Vietnam had a dispute with China over the strategic waterways, adding, "I am a very good mediator and a very good arbitrator and am willing to help", the local media reported.
Pacific Rim nation leaders agreed in Vietnam on Saturday to address "unfair trade practices" and "market distorting subsidies", a statement that bore the imprint of Trump's efforts to reshape the global trade landscape.
But on Sunday, Vietnam's state television said Chinese President Xi Jinping had told Vietnam's General Secretary, Nguyen Phu Trong, he wanted to work with Southeast Asian nations on a code of conduct in the sea. "Terrorism and violent extremism endanger the peace, stability, and security of our region because these threats know no boundary", he said.
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China and Vietnam need to "stay committed to seeking a fundamental and durable solution to their maritime issues acceptable to both sides through friendly consultation", Xi said in an article published by the state-run Xinhua news agency Thursday - before Xi's arrival in Vietnam.
Duterte - sometimes described as the "Trump of the East" because of his brash style - said last week he would tell the US president to "lay off" if he raised the issue of human rights when they met.
"You want to control the passage, or do we have free passage?"
"We have to be friends, the other hotheads would like us to confront China and the rest of the world on so many issues", Duterte said at a pre-summit business conference in Manila.
Philippines President Rodrigo Duterte, the host of the summit in Manila, responded to Trump's offer to help with the contested waterway.
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The President also grabbed the opportunity to thank Xi for the China weapons donated to the Filipino troops, saying these were used to help defeat the rebels in Marawi.
Trump will join leaders of Southeast and East Asian nations in Manila over the next two days, the last leg of a tour that has taken him to Japan, South Korea and China as well as Vietnam.
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.
The communist neighbours have long-sparred over the sea - to which Brunei, Taiwan and the Philippines also have partial claims - through which $5 trillion in shipping trade passes annually.
Vietnam has courted support from Washington in the row, in the face of Beijing's efforts in recent years to cement its claims by building artificial islands in disputed areas.
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