Lee said the recent shelling of Yeonpyeong Island marked a new level of aggression from North Korea, The New York Times reported.
"If the North commits any additional provocations against the South," he said, "we will make sure that it pays a dear price without fail."
Lee thanked the United States, Japan, Russia and other nations for condemning North Korea's artillery attack, which left four people dead and 16 injured on the island in the Yellow Sea near the disputed maritime border between the countries.
Lee said his country has provided North Korea with humanitarian aid and worked to reduce the threat of its nuclear weapons but the North has reacted with hostility. He cited the March sinking of a South Korean warship and the deaths of its 46 crewmen.
"I cannot help but be infuriated at the brutality of the North Korean regime," he said. "Our people have clearly come to know that any more endurance and tolerance will cultivate even bigger provocation."
Lee did not mention China's overtures to reduce tensions between the two Koreas. On Sunday China called for "emergency consultations" next month in Beijing with North Korea, South Korea, Japan, Russia and the United States, members of the so-called six-party talks aimed at denuclearizing North Korea.
Two polls indicate South Koreans are upset that China hasn't denounced North Korea's actions and criticized the United States for participating in military exercises with South Korea, the Times said. North Korea also called the joint exercises, scheduled by Seoul in response to the shelling, as provocative.
Asia experts in Washington were split about a response to China's proposal, the Times said. Some said the United States and South Korea would be forced to concur with China's call for talks if only to defuse the tension and prevent North Korea from taking even more aggressive action against the South.
"Ultimately, you have to talk with them," George Perkovich, an arms control expert at the Carnegie Endowment for International Peace, told the Times. "You have to bargain, because if you don't this is what they do. They make things worse. They create a crisis."
South Korean news agency Yonhap said a source in Beijing told it Monday a high-level Chinese foreign policy adviser, State Councilor Dai Bingguo, may visit North Korea soon. Dai was in Seoul Saturday to meet with Lee, and the Chinese Foreign Ministry said Monday Dai talked by telephone with U.S. Secretary of State Hillary Clinton.
State Department spokesman Philip J. Crowley said Clinton told Dai that North Korea's actions have been "destabilizing" and that "clear steps by North Korea are needed to demonstrate a change in behavior."
Swim Week Miami Beach 2014 [PHOTOS]