Duterte has long expressed his admiration for Xi and said he would raise the arbitration ruling with him eventually, but needed first to strengthen relations between the two countries, which the Philippines is hoping will yield billions of dollars in Chinese loans and infrastructure investments.
The Hague award clarifies Philippine sovereign rights in its 200-mile Exclusive Economic Zone to access offshore oil and gas fields, including the Reed Bank, 85 nautical miles off its coast.
It also invalidated China's nine-dash line claim on its maps denoting sovereignty over most of the South China Sea.
Duterte has a reputation for his candid, at times incendiary, remarks and his office typically backpeddles on his behalf and blames the media for distorting his most controversial comments.
Duterte recalled the same story about his discussion with Xi on oil exploration in a recorded television show aired moments after the speech.
He said Xi told him "do not touch it".
He said Xi had promised that the arbitration ruling would be discussed in future, but not now.
Duterte said China did not want to bring up the arbitral ruling at a time when other claimant countries, like Vietnam, might also decide to file cases against it at the arbitration tribunal.
It was not the first time the firebrand leader has publicly discussed the content of private meetings with other world leaders.
His remarks came the same day that China and the Philippines held their first session in a two-way consultation process on the South China Sea.
They exchanged views on "the importance of appropriately handling concerns, incidents and disputes involving the South China Sea", the Chinese Foreign Ministry said in a statement that gave few details.