The declaration is part of a broader multilateral deal under which North Korea, which apparently detonated an atomic device in October 2006, had agreed to abandon all its nuclear programmes in exchange for economic and diplomatic incentives.
Kim said: "The US needs more time, while North Korea's preparations are almost done."
Earlier last month, Christopher Hill, the top US negotiator with Pyongyang, said North Korea appeared close to making the declaration.
The declaration was held up also partly because of the North's reluctance to answer US questions that it transferred nuclear technology to other countries, notably Syria, and had a secret programme to enrich uranium for weapons.
Once the declaration has been produced, the US is expected to drop North Korea from its "terrorism" blacklist and end sanctions imposed under the US Trading With the Enemy Act.
North and South Korea, the US, China, Japan and Russia have been involved in long-running "six-party" talks aimed at curtailing North Korea's nuclear plans, a process that intensified after Pyongyang's nuclear weapon test in 2006.