The U.S. has made it "absolutely clear" to China that it will continue freedom of navigation operations in the disputed waters of South China Sea despite Beijing's objections, a senior Navy officer said.

The Chief of Naval Operations Adm. Mark Richardson said on Tuesday that the U.S. will continue engaging in flights and naval activities in the South China Sea, as the conflict continues based on a Hague ruling regarding the territorial claims in the waters.

The U.S. Secretary of State John Kerry said that the peaceful settlement of disputes in the South China Sea is "absolutely critical."

The U.S. "does not take a position on the side of one claimant or another claimant," Kerry told CNN.

Kerry added: "What we are pushing for is absolute support for rule of law, for the legal process, and for diplomacy to work out the differences that people have."

He also said that he had a "constructive meeting" with China's Foreign Minister Wang Yi at the ASEAN Regional Forum on how both the nations would proceed on this issue.

Earlier this month, an international tribunal in the Hague rejected China's vast territorial claims in the South China Sea and said it has no legal basis under the UN Convention on the Law of the Sea.

But China dismissed the court's verdict and said it would not affect its claims.