NEW YORK, Sept. 21 (Yonhap) -- South Korean President Lee Myung-bak and Japan's new prime minister, Yoshihiko Noda, agreed Wednesday to cooperate closely in dealing with North Korea and moving relations between the two countries forward as they held their first face-to-face talks in New York.

"I expect that Prime Minister Noda will contribute greatly to strengthening relations between the two countries," Lee said at the start of their talks on the sidelines of the U.N. General Assembly.

Noda said in response that continuity is important in diplomacy and his government will consider South Korea a very important neighbor as its predecessors did, and will continue to strengthen the friendly ties between the two countries.

The presidential office said in a release later that the two countries agreed to work together to improve their relations in a "mature, future-oriented manner while facing up to past history."

The relations between Seoul and Tokyo have often frayed over issues stemming from Japan's 1910-45 colonial rule of Korea, including Japan's territorial claims to South Korea's easternmost islets of Dokdo or its attempt to gloss over wartime atrocities.

On North Korea, the two leaders pledged to continue to work closely on North Korea based on a common understanding that policy coordination on North Korea is important not only for security of the two countries, but also for international peace and stability, the office said.

The leaders also agreed to continue cooperation on other matters, such as Japan's promise to return centuries-old Korean royal texts and creating the atmosphere for resuming free trade talks between the two countries, the office said.