JAKARTA—U.S. Secretary of State Hillary Clinton said Asian countries need to agree on a code of conduct defining how they will interact in disputed parts of the South China Sea to ease rising tensions in the region.

During a visit to Indonesia and a day before flying to meet with leaders of China, Mrs. Clinton said Monday that China and countries with competing claims in the South China Sea need to push for the long-delayed completion of a code of conduct to settle their differences.

"The...