SEOUL, South Korea — The leaders of China and South Korea sent a strong message to North Korea on Thursday, saying they were united in their opposition to the development of nuclear weapons on the Korean Peninsula, though they fell short on how they would pursue that goal.

After a three-hour meeting, China’s president, Xi Jinping, and South Korea’s leader, Park Geun-hye, issued a joint statement that smoothed over the differences in approach that have stalled a more aggressive stance toward the unabated development of nuclear weapons by North Korea, and its leader, Kim Jong-un, China’s ally.

Their joint communiqué said that the “two countries reaffirm their firm opposition to the development of nuclear weapons on the Korean Peninsula,” phraseology that the Chinese have always preferred because it does not specifically cite North Korea.

With Mr. Xi standing beside her, Ms. Park read a statement that said the two leaders had agreed that the “denuclearization of North Korea must be achieved at all costs,” with the emphasis on the nation of North Korea rather than the Korean Peninsula.