President Bush and South Korea's President Roh Moo-hyun say North Korea's nuclear weapons programs must be ended through diplomatic means.
In a joint statement Thursday in South Korea, the leaders declared that a nuclear-armed North Korea "will not be tolerated," and a solution should be reached peacefully.
The leaders spoke at a joint news conference in Korea's ancient capital, Gyongju.
On Friday, the two will travel to the southern port of Busan for the annual Asia-Pacific Economic Cooperation summit.
The conference is expected to encourage members of the World Trade Organization to break a deadlock over agricultural subsidies, and fight bird flu and terrorism.
Wednesday in Kyoto, Japan, Mr. Bush urged China to grant more political freedoms. He also praised Taiwan as an example of a successful democratic society.
China's Foreign Minister (Li Zhaoxing) later dismissed the remarks, saying China and Taiwan should not be talked about as separate entities.
Some information for this report provided by AP, Reuters.