Trump added he hoped Russian Federation would also "be a tremendous help". The disputes are expected to get the spotlight at the summit, along with the North Korean nuclear threat and terrorism.
In a statement released after the talks, China's foreign ministry said China and the U.S. had a "common goal" for the Korean peninsula, and that they would increase communication on the issue.
Days after the USA leader met with Xi in Beijing, Trump made a surprise offer to Vietnamese President Tran Dai Quang in Hanoi.
Trump's offer faces major obstacles. The dispute centers around the Spratly and Paracel Islands.
From Vietnam, Trump left for the Philippines - the last stop on his tour - for a meeting with leaders of the Association of Southeast Asian Nations (ASEAN).
Chinese President Xi Jinping met with Vietnamese Communist Party chief Nguyen Phu Trong during a state visit to Hanoi on Sunday, after Trump also visited the country.
"He acknowledged that war can not be promoted by anybody, (that) it would only mean destruction for all of us", Duterte told reporters after flying back to Manila.
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".
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.
The Philippines had been the most vigorous critic of Chinese territorial claims, but Philippine President Rodrigo Duterte has recently dialed back his country's objections, leaving Vietnam as the leading critic.
"If you go to the negotiating table and you start with the statement that I am here to claim validity of our ownership, you're wasting your time".
Ahead of his trip to Vietnam, Duterte said he would ask his Chinese counterpart what Beijing's intentions in the region are.
The framework will be endorsed by China and ASEAN members at a summit in Manila on Monday, a diplomat from one of the regional bloc's countries said.
While Trump may claim to want a closer relationship with Kim, only last week he told South Korea's parliament that the dictator has turned North Korea into "a hell that no person deserves". At least 20 protesters were injured in the brief scuffle and one was arrested, according to protest leaders, adding that the demonstrators dispersed after burning a mock US flag.