A spat between China and Vietnam over energy rights in the South China Sea intensified on Wednesday as Vietnam's biggest company called on China to scrap its plans to develop areas near the Vietnamese shore.

The disagreement, the latest in a string of arguments over the potentially energy-rich sea, erupted earlier in the week when China National Offshore Oil Corp. said it was offering a new batch of oil-exploration blocks inside the 200-nautical-mile exclusive economic zone granted to Vietnam under the United Nations' Law...