The United States and North Korea resumed nuclear weapons talks Sunday, with the chief U.S. negotiator hoping to nail down progress achieved in the first day. «We're going to try to summarize yesterday's discussion,» U.S. Assistant Secretary of State Christopher Hill said. «In particular, we want to make sure that we have a complete understanding about what the various meetings are going to look like.» Hill spoke with reporters before going to the North Korean Mission to U.N. offices in Geneva where he joined Kim Gye Gwan, the head of the North Korean delegation, for the second day of talks. Hill said Saturday evening that enough progress was made that he could look forward to a successful meeting later this month when both sides meet with Japan, Russia, South Korea and China in six-nation talks aimed at ending North Korea's nuclear weapons program and improving relations between North Korea and other countries. Hill said both countries still have a long way to go, the Associated Press reported. «But I think we reached substantial understanding between the two of us of what needs to be accomplished in the months ahead.» Kim said the first session had gone well, and «I expect this meeting will have a fruitful outcome.» Hill said Sunday that improving U.S. relations with North Korea will depend on other progress in the talks, saying it «is a relationship that we will continue to try to build step by step with the understanding that we're not going to have a normalized relationship until we have a denuclearized North Korea.» «To the extent that we can move quickly to denuclearization, we can move quickly to normalization,» he added.