The leaders also warned North Korea they will not tolerate further nuclear tests, amid fears that Pyongyang is preparing a third atomic blast.
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.
Chinese Premier 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," Wen told reporters in Beijing.
"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 have the world's largest economy, ahead of the European Union, when measured by purchasing power parity.
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," South Korea's Lee said.
A free-trade area among Northeast Asia's three major economies 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 the issue.