Wang responded by saying China was open to discussing that possibility with the Philippines "but not in the context of the arbitral tribunal ruling", Yasay said.
Phillippines welcome the decision of worldwide court.
Yasay's account of the meeting highlights the challenge ahead for the Philippines, a USA ally, in getting China to comply with the decision which has ramped up tensions in the vital trade route.
The Philippine government disagrees and has support from other countries bordering the sea and equally exposed to Chinese claims, including Indonesia, Malaysia, Brunei, Taiwan and Vietnam.
Vietnam has welcomed the ruling, but not said whether it will pursue the same legal path as the Philippines.
"We will never stop our construction on the Nansha Islands halfway... the Nansha Islands are China's inherent territory, and our necessary construction on the islands is reasonable, justified and lawful", Wu said.
"Similarly, the arbitrary tribunal does not have the right to resolve this dispute", he said.
State media also reported the head of China's navy saying on Monday that China will not halt the construction of islands and reefs in the South China Sea.
Senior Colonel Zhang Junshe says, "All the countries around the South China Sea, we are a community".
Following his visit in Beijing, Richardson is scheduled to visit China's North Sea Fleet for a visit the Chinese Navy's submarine academy and tour the aircraft carrier Liaoning (CV-16).
Footage showed the Filipino boat being tailed by a white Chinese coast guard ship and Chinese personnel using a bullhorn to order the Filipinos to leave "this area immediately".
China has refused to recognize last Tuesday's ruling and did not take part in its proceedings.
Schoff added that while the US was not seeking out conflict, it would continue its own demonstrations in the region, potentially boosting the risk of "unsafe" encounters at sea and in the air. He has ordered government lawyers to study the ruling and has not disclosed his plan to secure Chinese compliance. Such a move would be seen as a threat to freedom of navigation, which the US has promised to uphold. "Coastal states like the Philippines are entitled to what we call the exclusive economic zone, which is equivalent to 200 nautical miles, whereby the coastal state has the right to explore, exploit the resources within that zone". "This would depend on our overall assessment", Liu said.
China defiantly announced Monday it will militarily close off parts of the South China Sea to conduct war drills, a week after an worldwide tribunal denied China's historic claims to the majority of the region.
The U.S. has also flown A-10C attack planes through global airspace in the vicinity of Scarborough Shoal, just 230 km west of the Philippines.
China didn't want any mention of the South China Sea at a summit of Asian and European leaders in Ulaanbataar, the Mongolian capital.
In a separate message on its website, the maritime administration said last week that four out of five lighthouses built atop islands and reefs in the sea have been activated, and a fifth would be put into use soon.