Cayetano said the two countries must work together to safeguard peace and ensure stability in the South China Sea.
Several Vietnamese fishing vessels escaped Indonesian interception in May following a show of force by Vietnam's coast guard in the South China Sea, where China's expansive territorial claims overlap with the waters of several Southeast Asian nations.
Chinese Foreign Minister Wang Yi, visiting Manila on Tuesday, said Beijing was open to joint development.
We sincerely hope so.
Secretary Cayetano said although it is not stated in the Constitution of the Philippines, he believes it can still be done.
Confrontations have boiled between China and the USA for the past few years over the disputed region.
That might lead to tensions, and as the result, nobody might be able to develop the resources, Wang said.
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He has downplayed the Philippines' dispute with China and said better relations with China will generate billions of dollars in investment and aid.
China claims nearly all of the South China Sea, through which trade worth an estimated $5tn (£3.9tn) passes each year.
Taiwan also claims nearly the entire area, which is believed to sit atop vast oil and gas reserves, but is not an Asean member.
Negotiations for a joint exploration had "peaked" during Duterte's visit to Beijing in May, when he told Chinese President Xi Jinping that he meant to drill for oil in the South China Sea, according to Cayetano.
China took full control of the Paracels in 1974 after a naval showdown with Vietnam. "There's no difference to us because both of them are saying it's not ours", he said.
Cayetano said the U.S. speaks very firmly on the United Nations Convention on the Law of the Sea (UNCLOS) but Washington should not interfere in the Philippines' strategy in the West Philippine Sea because the USA is not even a signatory to UNCLOS.
"China has repeatedly assured us that those (missiles) are for defense". Vietnam, Indonesia, the Philippines, Malaysia and Brunei all lay claim to islands in the region - territorial aspirations that have both sown division in Asean and drawn the ire of Beijing, despite an global tribunal in The Hague ruling against China's territorial claims in the sea.
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