Story highlights John Kerry meets with his Chinese counterpart

South China Sea dispute, North Korea tensions overshadow meeting

Washington (CNN) Secretary of State John Kerry and his Chinese counterpart locked horns over a range of issues Tuesday, agreeing to disagree in a State Department press conference over South Korean missile defense and the contested South China Sea.

But Kerry also pointed to an area of progress: nearing agreement on a U.N. Security Council resolution on North Korea's nuclear test. Even so, he defended the possible U.S. deployment of advanced THAAD missiles to defend South Korea and called for de-escalation as China and its neighbors compete over nearby islands.

The back-and-forth between Kerry and Chinese Foreign Minister Wang Yi reflected the awkward dance of competition and cooperation between the United States and China. The world's two largest economies work together on issues like Iran's nuclear program, the civil war in Syria and climate change, even as they clash over cybertheft, North Korea's nuclear ambitions, missile defense in South Korea and how to handle contested stretches of ocean in Asia.

And it came as U.S. officials confirmed that China has deployed fighter jets, J--11s and J-7s, to the disputed Woody Island. U.S. officials told CNN it was not the first time China has placed fighter jets on the island after expanding the runway there in 2014.

"We can cooperate in areas where our interests and values are aligned despite the fact that we have differences," Kerry said, while Wang said the United States and China "should make the cake or the pie of our common interests bigger."

Read More