South Korea is promising North Korea what it calls a new, substantial proposal if the North returns to six-party disarmament talks.
South Korean officials made the offer Monday, but did not elaborate, as the two sides held their first working-level negotiations in 10 months at the North's border town of Kaesong.
The North did not respond to the nuclear comments, but requested fertilizer aid from the South and said it also needs food aid. The talks come after the United States and Japan warned they will punish North Korea if it conducts nuclear testing.
U.S. National Security Adviser Stephen Hadley said Sunday a nuclear test would be a serious act of defiance and that "action would have to be taken."
Earlier, Japan's ruling party chief Shinzo Abe said Tokyo would call for U.N. economic sanctions against North Korea if it carries out a nuclear test.
Information for this report is provided by AP and Reuters.