Lee Myung-Bak made the remark after talks in Beijing with Chinese Premier Wen Jiabao and Japanese Prime Minister Yoshihiko Noda that also saw the trio decide to start free-trade area negotiations before the end of this year.
"Our three countries agreed that we will not accept further nuclear tests or further provocations from North Korea," Lee told reporters after meeting with his two counterparts for 90 minutes.
The Northeast Asian leaders had been expected to put Pyongyang's nuclear and rocket programmes high on the agenda for Sunday's summit.
Fears of a third North Korean nuclear test have grown after a failed rocket launch by Pyongyang last month that the United States and its allies said was a disguised ballistic missile test banned under UN resolutions.
Satellite photos have recently shown work in progress at the Punggye-ri nuclear test site.
Noda called on the three countries to strengthen co-operation in order to "further prevent provocations" by North Korea in future.
Wen warned earlier Sunday that the region faced many "unstable" factors that made the situation hard to predict.
"The various parties need to use their wisdom, keep patient, and display goodwill to the greatest extent so as to ease confrontation and return to the right track of dialogue and negotiations," the Chinese premier said.
China, long the North's key ally, has been an advocate of seeking to put a stop to the isolated regime's nuclear ambitions via multilateral talks.
The three leaders also agreed to start talks this year on a free-trade area, saying it would boost the economies of the entire region.
The issue has been on the trilateral agenda for the past decade, beginning with an agreement among the three in late 2002 to launch a feasibility study on a free-trade area.
Wen said closer regional economic integration, in response to a slow global recovery and an overall rise in trade protectionism, would help unlock new growth potential.
"Northeast Asia is the most economically vibrant region in the world. So there is huge potential for our three countries to have closer trade and investment cooperation," he told reporters.
"The establishment of a free-trade area will unleash the economic vitality of our region and give a strong boost to economic integration in East Asia."
China, Japan and South Korea combined would have the world's largest economy -- ahead of the European Union -- when measured by purchasing power parity, which takes into account differences in living costs across nations.
"Today, as we look at the global financial crisis, some countries are still pursuing protectionist ideas and have expanded them," South Korea's Lee said.
"I'm worried about this. By comparison, I believe the agreement between the three countries is an important thing."
In Sunday's meeting, the three nations also signed an investment agreement concluded earlier this year after 13 rounds of negotiations stretching over five years.
"To further facilitate mutual investment, it is important to have a legal framework. It will help our businesses and mutual investment," Lee said.
Later in the day, Wen met Noda for bilateral talks, with both sides pledging to push ties between the world's second- and third-largest economies further.
"Both sides must seize the opportunity, increase mutual trust... and push forward the healthy and stable development of relations between the two countries," Wen told his Japanese visitor.