The statement is designed to end debate over its nuclear status and add pressure on Washington to make a statement of its own over Pyongyang's atomic ambitions.
A North Korean Foreign Ministry spokesman criticised calls for a fresh round of six-way nuclear talks, saying such discussions were meaningless unless Washington dropped its hostility toward Pyongyang.
“When an appropriate time comes, the DPRK will take a measure to open its nuclear deterrent to the public as a physical force and then there will be no need to have any more argument," the ministry spokesman said, noting some people doubted the North had nuclear capability.
US officials said that on the sidelines of talks in Beijing in April, a North Korean envoy had threatened that Pyongyang would demonstrate a nuclear weapon.
But Thursday's statement, the first time the North made the threat public, did not spell out how Pyongyang might display its deterrent.
It appeared to address comments last week by US Secretary of State Colin Powell that Washington had drafted new ideas on security assurances to offer reclusive North Korea.
Powell said Washington envisaged a public written document, preferably signed by some of North Korea's neighbours, but not the formal non-aggression treaty which Pyongyang demands.
If the United States put off dealing with the issue, "during that time the DPRK will have enough time to perfect and strengthen necessary means which has already been opened to the public", said the spokesman.
“When an appropriate time comes, the DPRK will take a measure to open its nuclear deterrent to the public as a physical force"
North Korean Foreign Ministry spokesman
China, Russia, the two Koreas, Japan and the United States held an inconclusive first round of talks in Beijing in late August.
All sides pledged to avoid steps that would aggravate the year-old dispute. But early this month, Pyongyang said it had redirected plutonium extracted from thousands of spent nuclear fuel rods to help enhance its deterrent force.
North Korea has said for the past year it faces an imminent threat of armed attack from the United States. Pyongyang wants Washington to sign and ratify a non-aggression treaty before it will dismantle its banned nuclear arms programmes.
North Korea has in the past increased the intensity of its rhetoric before returning to talks.