China claims nearly the entire South China Sea, while Taiwan, Vietnam, the Philippines, Malaysia and Brunei all believe they have rights to certain parts.
"China's greatest hope is for peace and stability in the South China Sea", Li told ASEAN leaders in Manila.
Reefs and islands in the South China Sea are disputed by Brunei, Indonesia, Malaysia, the Philippines and Taiwan, as well as China and Vietnam.
"Important that we cooperate to maintain peace, stability, freedom of navigation in and over-flight above the SCS (South China Sea), in accordance with global law", it said.
When he raised concerns over China's increasing military capability in the South China Sea, Duterte said Xi replied, "No, it's nothing".
Trump told Vietnam's President Tran Dai Quang that he was prepared to mediate between claimants to the South China Sea and said China's position was a problem.
The agreement came at a meeting between Chinese President Xi Jinping and Vietnamese Communist Party chief Nguyen Phu Trong in Hanoi.
The framework will be endorsed by China and members of the Association of Southeast Asian Nations (ASEAN) at a summit in Manila on Monday, a diplomat from one of the regional bloc's countries said.More news: Timothy Piazza Hazing Death
"Li said China is the largest country in the South China Sea and a major nation that uses the lanes in the sea, thus China shows more interest in safeguarding peace, stability, and navigation freedom in the South China Sea than any other country in the world", Xinhua said.
Philippine Foreign Affairs Secretary Alan Peter Cayetano did not directly answer when asked about Trump's offer.
The stop in the Philippines is the last leg of a tour that has taken Trump to Japan, South Korea and China as well as Vietnam, the longest Asia trip by a USA president in more than 25 years.
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. "So if I can help you, let me know".
To mend the strained relations of the Philippines and China, Duterte, who came into power in 2016, chose to temporarily set aside the arbitration ruling.
"While the situation is calmer now, we can not take the current progress for granted", said the draft, a copy of which was seen by Reuters.
Philippine Defense Secretary Delfin Lorenzana said last week that the dispute over a string of sandbars called Sandy Cay emerged in August and prompted China and the Philippines to consider negotiating some sort of protocol or arrangement to allow both sides to prevent such incidents from spiraling out of control. He has refused to immediately take up with China a ruling by a United Nations -linked tribunal that invalidated Beijing's sprawling claims in the South China Sea, sparking criticism from nationalists and left-wing groups that wanted him to demand Chinese compliance with the landmark decision immediately.