Dotted with small islands, reefs and shoals, the South China Sea is a crucial shipping route and home a messy territorial dispute that pits multiple countries against one another.
The framework will be endorsed by China and the 10-member Association of Southeast Asian Nations (ASEAN) on Monday, a diplomat from one of the regional bloc's countries said.
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.
In a joint news conference, Quang said he had "shared my thoughts with (Trump) on the recent developments in this area and it is our policy to settle disputes in the South China Sea through peaceful negotiations, and with respect for diplomatic and legal process in accordance with worldwide law, including the 1982 UN Convention on the Law of the Sea".
Trump is telling President Tran Dai Quang he knows Vietnam has had a dispute with China over the strategic waterways.
Trump added he hoped Russian Federation would also "be a tremendous help".
China, Taiwan, Vietnam, the Philippines, Malaysia and Brunei all have competing claims to various island chains in the South China Sea.
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China has been urged by both South Korea and the United States to take a more active role in curbing North Korea's nuclear and missile ambitions. The Hague rejected China's territorial claim to the maritime area in 2016 and found in favour of the Philippines, but China rejected the ruling. "We have to be friends. It can ill-afford a violent confrontation". "The South China Sea is better left untouched".
While Manila appreciates Trump's "honest" offer, Cayetano said claimant countries in the contested waters must first give their take on the proposal.
"The discussions focused on cooperation based on their converging vision and values for promotion of peace, stability and prosperity in an increasingly inter-connected region that they share with each other and with other partners", the ministry of external affairs (MEA) said. The menace of illegal drug trade continues to endanger the very fabric of our society.
The Philippines values its friendship with China "more than anything else", President Duterte assured Chinese President Xi Jinping during their meeting in Vietnam.
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.
Others who will be in Manila for the summit meetings include Chinese Premier Li Keqiang, Russian Prime Minister Dmitry Medvedev and leaders from Japan, Canada, South Korea, India, Australia and New Zealand. China's move to pressure Vietnam to stop oil drilling in a disputed area in July brought relations between the Communist neighbours to a low.