South and North Korea have failed to narrow their differences on ways to resume the six-party talks on North Korea's nuclear disarmament.

Nuclear envoys for the two Koreas met Wednesday in Beijing for their second round of talks in the past two months.

South Korea said the North must halt its uranium-enrichment program and take other concrete steps for its denuclearization before the talks resume. North Korea wanted the talks to resume without preconditions.

After the talks, South Korean negotiators Wi Sung-lac said the meeting was significant because the two sides were able to resolve some mutual misunderstandings. North Korea's Ri Yong Ho called the talks constructive and useful.

In New York, South Korean President Lee Myung-bak expressed hope for peace and prosperity in North Korea. He said that goal will be advanced as Pyongyang becomes “a responsible member of the international community.”

Mr. Lee made his comments in his address to the U.N. General Assembly. He said South Korea will lead international efforts to ensure improved conditions in the North, when Pyongyang chooses “the path to mutual benefit and common prosperity.”

South Korean Yonhap news agency says Mr. Lee discussed North Korea during a meeting with Japan's new prime Minister Yoshihiko Noda in New York.

Japan, China, Russia and the United States are also parties in the six-nation talks on North Korea's nuclear disarmament.

North Korea abandoned the talks in 2009, but has been pressing, with China's backing, for a resumption of talks.