"If I can help mediate or arbitrate, please let me know", Trump said in comments at a meeting in Hanoi with Vietnam's president, Tran Dai Quang.
The framework seeks to advance a 2002 Declaration of Conduct (DOC) of Parties in the South China Sea, which has mostly been ignored by claimant states, particularly China, which has built seven man-made islands in disputed waters, three of them equipped with runways, surface-to-air missiles and radars.
Despite unresolved issues, discussions between ASEAN and China have improved, Cayetano said.
China and Vietnam have reached a consensus on appropriately handling the contested South China Sea.
The communist neighbours have long sparred over the sea, through which $5 trillion in shipping trade passes annually and which is believed to sit atop vast gas reserves.
The two parties said it "is important that we cooperate to maintain peace, stability, freedom of navigation in and overflight above the SCS, in accordance with global law", including the 1982 United Nations Convention on the Law of the Sea (UNCLOS). Duterte took steps to thaw frosty relations with China after he won the presidency previous year.
The Asean summit opens on Monday under extra-tight security at a theatre and convention complex by Manila Bay. It announces that both sides have agreed to officially start negotiations on the code.
"We hope non-regional countries can respect the regional countries' efforts in maintaining the regional stability of the South China Sea, and play a constructive role in this aspect", foreign ministry spokesman Geng Shuang said at a regular press briefing in Beijing.
We'll update this story as it continues to develop.
"If that did happen, it would be a good thing, I can tell you, for North Korea".
The two leaders met on the sidelines of the Asia-Pacific Economic Cooperation (APEC) summit in the Vietnamese resort city of Danang.
The President also told Turnbull how Xi seemed to be surprised by Duterte's new stand on the South China Sea issue and how the Chinese President downplayed the militarization in the disputed waters.
When he raised concerns over China's increasing military capability in the South China Sea, Mr Duterte said Mr Xi replied, "No, it's nothing".
Vietnam has become the most vocal opponent of China's moves after Philippine President Rodrigo Duterte softened his country's stance on China.
According to Malacañang, Duterte recognized the strong relations between the Philippines and Brunei and vowed to further strengthen it in the years ahead.