WASHINGTON—Secretary of State Mike Pompeo and Defense Secretary Jim Mattis met Friday with their Chinese counterparts, agreeing in principle to denuclearize the North Korean Peninsula but clashing over the South China Sea, Taiwan and human rights.

“This was an incredibly productive conversation,” Mr. Pompeo said after the meeting in Washington. “The United States is not pursuing a Cold War or containment policy with China, rather we want to ensure that China acts responsibly and fairly.”