China has insisted that issues relating to sovereignty and maritime delimitation are subject to third-party arbitration.
United States officials say the U.S. response should China stick to its vow to ignore the ruling could include stepped up freedom-of-navigation patrols close to Chinese claimed islands in what is one of the world's business trade routes.
China hopes the United States "speaks and acts cautiously, and takes no actions that harm China's sovereignty and security interests", Mr Wang said, according to the statement by the Chinese Foreign Ministry.
US officials have said Washington could respond to Chinese nonobservance of the court ruling with increased freedom-of-navigation patrols close to the islands.
In 2013, the Philippines filed suit with the Permanent Court of Arbitration, established under the United Nations Convention on the Law of the Sea.
The U.S. State Department confirmed that Kerry had spoken by phone to Wang.
"Our Secretary of Defence and the President himself regularly list the South China Sea among the world's most concerning global friction points and raise it at the highest levels with their Chinese interlocutors, including Chinese President Xi Jinping", he said.
Feng said that Taiwan is continuing to monitor developments regarding the South China Sea, including any moves being taken by related countries such as China, and he expressed hope that no conflicts will arise. "China is a peace-loving country and deals with foreign relations with discretion, but it won't flinch if the USA and its small clique keep encroaching on its interests on its doorstep", state-run Global Times said in an editorial today. The Chinese characters read, "Peaceful South China Sea".
The tribunal said last week that it will announce its ruling on the Philippines' case against China over the South China Sea disputes on July 12. Ambassador Yparraguirre emphasized in her statement, pointing out that, "This [arbitral] award will be the rule of law on this dispute".
He also made it clear that China will not accept any proposal or action by any country based on the ruling of the arbitration court.
China claims almost all the South China Sea, but its claims overlap in part with those of Brunei, Malaysia, the Philippines, Taiwan and Vietnam.
Shannon Ebrahim, a well-known South African commentator, said on Friday that United States of America intervention in the South China Sea issue has aimed to serve its goal to impede China's rise.
"This has always been China's policy, and it will never change".
Kerry said the U.S. understands that China has its own stance on the arbitration.
"The PLA has held similar exercises in the same general area of the South China Sea and declared a similarly large section off limits".
U.S. naval officials said Chinese military ships and some fishing vessels often track the activity of USA ships in the area, but there has been no reaction to the destroyers' operations.