Vietnamese President Tran Dai Quang said his country wanted to end disputes in the South China Sea through peaceful means.
Mr Trump's offer faces major obstacles, as China has steadfastly opposed what it calls USA meddling in the disputes and is unhappy about the USA navy's incursions into what Beijing considers its territorial waters in the South China Sea.
"If I can help mediate or arbitrate, please let me know..."
He also said that China was helping to resolve tensions over North Korea and added he hoped Russian Federation would do the same.
Unlike China, the USA is not a claimant to the potentially oil-rich and busy waters, but it has declared it has a national interest in ensuring freedom of navigation and overflight and the peaceful resolution of the disputes.
Southeast Asian nations will not take a relative calm in the dispute over the South China Sea for granted, according to a draft of a statement to be issued during a summit meeting in Manila on Monday.
China has steadfastly opposed what it calls United States meddling in the dispute over waters also claimed by several South-east Asian nations, and has baulked at the USA navy's incursions into what Beijing considers its territorial waters.
A source familiar with the investigation told ESPN that the players could be required to stay in china for up to two weeks.
"We want to get that straightened out very quickly", Trump said at a meeting with Prime Minister Nguyen Xuan Phuc.
"We're also concerned about what's happening in the South China Sea - the continued buildup of military installations, and in our bilateral last night with Mr. Xi Jinping, I told the President our misgivings", Duterte told Turnbull.
"He acknowledged that war can not be promoted by anybody, (that) it would only mean destruction for all of us", Mr Duterte told reporters after flying back to Manila.
"The South China Sea is better left untouched, nobody can afford to go to war".
China has dismissed that ruling as a "sham" and did not participate in the arbitration case that the Philippines filed during the administration of Mr Duterte's predecessor. At $32 billion previous year, it was the sixth largest with the United States, though less than a tenth the size of China's. "They will not talk about it", Duterte said of China.
"I am not saying there are no problems; I am saying it is getting better", he added.
Leaders of the ASEAN also will sign an accord aiming to protect migrant workers from the poverty-wracked region during a two-day summit that opened Monday in Manila, according to a draft of a post-summit communique seen by The Associated Press.
Riot police used shields and water hoses on Sunday to push back hundreds of left-wing activists who tried to hold a protest at the US Embassy and carried placards that read "Ban Trump".