Opening two days of high-level U.S.-China talks in Beijing, Clinton said North Korea must be held to account for the incident, which international investigators have determined was caused by a torpedo fired from a North Korean submarine.
China is North Korea's main ally and has thus far remained neutral on the investigation. U.S. officials say they have more work to do to convince China that North Korea was responsible for the ship sinking.
Clinton called the situation with North Korea a "matter of urgent concern."
"Today, we face another serious challenge provoked by the sinking of the South Korean ship. So we must work together ... to address this challenge and advance our shared objectives of peace and stability on the Korean peninsula," she said.
"We ask North Korea to stop its provocative behavior, halt its policy of threats and belligerence toward its neighbors and take irreversible steps to fulfill its denuclearization commitments and comply with international law," Clinton said.
In Seoul, South Korean President Lee Myung-bak said his country will take the case to the U.N. Security Council on Monday. "North Korea will pay a price corresponding to its provocative acts," he said. "I will continue to take stern measures to hold the North accountable."
Clinton also called on China to continue work with the United States and other members of the U.N. Security Council to draft new sanctions on Iran to press it to come clean on its nuclear program. She said "the burden is on Iran" to prove its nuclear program is peaceful and avert fresh penalties.
Clinton was joined onstage at China's Great Hall of the People by Treasury Secretary Timothy Geithner and Chinese Vice Premier Wang Qishan and State Councilor Dai Bingguo, all of whom spoke. Neither Wang nor Dai specifically mentioned North Korea or Iran, but Dai made clear in that China would not support any attempt to provoke conflict.
"No attempt to stir up confrontation and stage war, be it a hot war, a cold war or even a warm war, will be popular in today's world," he said. "Nor will such an attempt lead to anywhere."
Similarly, Chinese President Hu Jintao, who also addressed the opening session, did not mention North Korea by name but spoke of the responsibilities shared by the United States and China for "managing regional hotspots" and "safeguarding world peace and security."
He also said the countries should "step up communication and coordination on regional hotspot issues" in both bilateral and international forums.
On the broader relationship, each of the speakers talked about the need to conduct business on "win-win basis," where the two sides look at each other not as rivals but as partners.
"Few global problems can be solved by the United States or China acting alone and few can be solved without the United States and China working together," Clinton said.
