South Korea and China will closely work together to push for a peace treaty with North Korea that would formally end the Korean War, the countries' leaders said Friday, Yonhap News reported.

In a telephone conversation with Chinese President Xi Jinping, South Korean President Moon Jae-in also stressed the importance of China's role in ridding North Korea of its nuclear ambitions, Moon's presidential office Cheong Wa Dae said.

"President Moon stressed that President Xi's continued interest and support, as well as the Chinese government's active contribution, are important in completely denuclearizing the Korean Peninsula and establishing permanent peace," it said in a press release.

The Moon-Xi conversation came one week after the South Korean president held a historic summit with North Korean leader Kim Jong-un at the border village of Panmunjom inside the Demilitarized Zone that divides the two Koreas.

In a joint statement, called the Panmunjom Declaration, Moon and Kim agreed to push for complete denuclearization of the Korean Peninsula and a formal end to the 1950-53 Korean War with a peace treaty.