South Korean President Park Geun-hye and Chinese President Xi Jinping came to the agreement hours after Park arrived in Beijing Thursday for a four-day visit, Yonhap news agency reported.
"We shared an understanding that North Korea's possession of nuclear weapons cannot be tolerated under any circumstances and confirmed that realizing the denuclearization of North Korea and maintaining peace and stability on the Korean Peninsula conform to the common interests of the two countries," Park said during a joint news conference with Xi.
Xi said he and Park have agreed to work together to denuclearize North Korea.
During her stay in China, Park is scheduled to speak at a university in Beijing, with part of the address delivered in Mandarin.
In a commentary Thursday, Xinhua, China's official news agency, said: "Though economic issues and cultural exchanges would be high on Park's agenda during her China trip, the situation on the Korean Peninsula is the topic that would capture most global attention."
China is the closest ally of North Korea, an impoverished and isolated Communist country whose nuclear and missile tests in violation of U.N. Security Council sanctions have sharply raised tensions on the peninsula. Until recently, the North, led by its unpredictable leader Kim Jong Un, also had been issuing highly provocative and dangers nuclear and other threats against the South as well as the United States.
In an interview with China Daily, Park was quoted as saying while the North's "provocations will be met with stern responses, the door for dialogue between the two Koreas will remain open." She said if the North chooses to "become a responsible member of the international community, the South will redouble its efforts to provide assistance and accomplish common prosperity in both the South and North."
China is reported recently to have pressured Pyongyang to moderate its stand and engage with the South and the United States, as Beijing seeks to restart the stalled Six-Party talks to convince the North to give up its nuclear program in return for massive aid. Besides the two Koreas, China and the United States, the Six-Party also includes Japan and Russia.
"The tense atmosphere surrounding the Korean Peninsula eased slightly last week after senior diplomats from the Democratic People's Republic of Korea (the official name of North Korea) said the country was ready to join in any form of talks, including the long-stalled six-party talks," Xinhua said. "For Park, who promised on her campaign trail and in her inauguration speech to build trust with Pyongyang, now faces an opportunity to do so."
Ahead of Park's visit, the foreign ministers of China and South Korea held their sixth strategic dialogue in Beijing. Later, Chinese Foreign Ministry spokesman Hong Lei quoted Chinese Vice Foreign Minister Zhang Yesui, who attended the talks, as saying China is ready to work with South Korea to ensure the success of Park's visit and that China takes a firm stand on the denuclearization issue.
South Korea's Yonhap News Agency said a record 71 business leaders are accompanying Park on the China trip, adding the number is much larger than the 51 when Park visited the United States in May.
Chinese media have been stressing China is South Korea's largest trading partner, while it remains a major destination of South Korean investment and a primary source of foreign tourists. Chinese official figures say annual bilateral trade reached $256 billion last year and the volume is expected to grow further as the two sides seek to have a free trade agreement.
In her interview with China Daily, Park said, "I believe it is high time for our two countries to seek a new framework of economic cooperation commensurate with our economic status in the international community."
Yonhap said experts would closely watch the Park-Xi summit to find out the extent to which China goes in its commitment to end North Korea's nuclear program.
In his meeting with U.S. President Barack Obama in Los Angeles this month, Xi said the North should give up its nuclear weapons aspirations.
"The North Korean nuclear issue is not easy," a South Korea presidential official told Yonhap. "But what is for sure is that there will be fairly in-depth discussions. ... There will be good discussions as the two countries share the common goal of resolving the North Korean nuclear issue."
Some analysts told Yonhap Beijing may be concerned the North's nuclear program may encourage Japan to build up its military power, triggering a regional arms race. Other analysts, however, said China may continue with the status quo as any instability in the North could affect its economic growth, set off a large influx of refugees and bring about a unified Korean Peninsula under South Korean and U.S. control across its border.