The Bush administration dismissed Kim's overture and described the offer to return to the talks as "just more North Korean rhetoric," saying they weren't being taken seriously.
Kim also said "if the regime's security is guaranteed, there is no reason to possess a single nuclear weapon," according to South Korean Unification Minister Chung Dong-young, who returned to Seoul after meeting the North Korean leader in Pyongyang.
North Korea announced earlier this year it possesses nuclear weapons, but Kim said Pyongyang would rejoin the Nuclear Nonproliferation Treaty and allow inspections by the U.N. nuclear watchdog agency if the nuclear standoff was resolved, Chung told a news conference.
North Korea pulled out of the treaty after the latest nuclear crisis erupted in late 2002, when U.S. officials accused the North of running a secret uranium enrichment program in violation of an earlier agreement between the two countries.
The North Korean leader also offered an olive branch to Washington amid the usually heated rhetoric between the sides, saying he "has no reason to think badly" of President Bush, Chung said.
The Bush administration called Kim's statement as "more North Korean rhetoric."
"We've placed no preconditions on North Korea returning to the talks," a senior administration official said, speaking on condition of anonymity. "North Korea needs to return to the talks, return to the table and be ready to negotiate in a serious manner."
At the State Department, spokesman Sean McCormack added: "The fact remains that North Korea needs to return to the talks, without preconditions, and engage in discussions in a constructive manner."
Bush recently referred to Kim using the honorific "Mr." — a softened tone after earlier comments labeling the North Korean leader a "tyrant" and lumping his country in an "axis of evil" that included Iran and Saddam-era Iraq.
The North has boycotted nuclear talks with China, Japan, Russia, South Korea the United States for nearly a year, citing "hostile" U.S. policies.
But Chung said Kim told him "if it is certain that the United States is respecting the North as a partner, North Korea could come to the six-party talks as early as July, but it has to be further negotiated with the United States."
On Friday, Kim said North Korea "was trying to stand against the United States because it looked down on us," according to Chung. "North Korea has never given up or refused the six-party talks," Kim said.