The threat came a day after the UN Security Council agreed to censure and sanction the Pyongyang regime for a rocket launch in December that breached international rules.
The country's National Defence Commission said: "We are not disguising the fact the various satellites and long-range rockets we will fire, and the high-level nuclear test we will carry out, are targeted at the US."
North Korea is believed by South Korea and other observers to be technically ready for a third nuclear test, and the decision rests with leader Kim Jong-un who pressed ahead with the December rocket launch in defiance of the UN sanctions.
China, the one major diplomatic ally of the isolated and impoverished state, agreed to this week's US-backed resolution. It also supported resolutions in 2006 and 2009 after Pyongyang's two earlier nuclear tests.
The statement by North Korea represents a huge challenge to Beijing as it undergoes a leadership transition, with Xi Jinping due to take office in March.
China's Foreign Ministry called for calm and restraint and a return to six-party talks. But it effectively singled out North Korea, urging the "relevant party" not to take any steps that would raise tensions. North Korea has rejected proposals to restart talks about its nuclear capacity. The US, China, Russia, Japan and the two Koreas are the six parties involved.
Analysts said Pyongyang could test as early as February – as South Korea prepares to install a new, untested president – or it could stage a nuclear explosion to coincide with former ruler Kim Jong-il's birthday on February 16.
Lee Seung-yeol, senior research fellow at Ewha Institute of Unification Studies in Seoul, said: "North Korea will have felt betrayed by China for agreeing to the latest UN resolution and they might be targeting China as well [with this statement]."
Washington has urged North Korea not to proceed with a third test. Glyn Davies, the US envoy for North Korean diplomacy, said: "Whether North Korea tests or not is up to North Korea. We hope they don't do it. We call on them not to do it. This is not a moment to increase tensions on the Korean peninsula."
The North was banned from developing missile and nuclear technology under sanctions dating from its 2006 and 2009 nuclear tests.
A South Korean military official said the concern now is that Pyongyang could undertake a third nuclear test using highly enriched uranium for the first time, opening a second path to a bomb.
North Korea's 2006 nuclear test using plutonium produced a puny yield, equivalent to one kiloton of TNT – compared with 13 to 18 kilotons for the Hiroshima bomb. US intelligence estimates put the 2009 test's yield at roughly two kilotons.
North Korea is estimated to have enough fissile material for about a dozen plutonium warheads, although estimates vary, and intelligence reports suggest it has been enriching uranium to supplement that stock.
According to estimates from the Institute for Science and International Security from late 2012, North Korea could have enough weapons grade uranium for up to 32 nuclear weapons by 2016 if it used one centrifuge at its Yongbyon nuclear plant to enrich uranium to weapons grade.
North Korea's long-range rockets are not thought capable of reaching the United States mainland and it is not believed to have the technology to mount a nuclear warhead on a long-range missile.
Pyongyang's bellicose statement appeared to dent any remaining hopes Kim Jong-un, believed to be 30 years old, would pursue a different path from his father Kim Jong-il, who oversaw the country's military and nuclear programmes.
The older Kim died in December 2011.