Pyongyang was responding to the decision by the United Nations nuclear watchdog to refer it to the UN Security Council for breaching nuclear non-proliferation agreements.
Amid mounting tension Japan warned that it would "use military force as a self-defence measure" if North Korea started to "resort to arms against Japan".
Japanese Defence Minister Shigeru Ishiba added that such a defensive move would not amount to a pre-emptive strike.
North Korea's latest threat comes a day after the head of the US Central Intelligence Agency, George Tenet, warned that Pyongyang had a long-range missile capable of reaching the west coast of America.
North Korea's comments are a typically bellicose response from the secretive communist state, says the BBC's correspondent in Seoul, Caroline Gluck.
Warning
A senior official in Pyongyang, Ri Kwang-hyok, told the AFP news agency: "In case there is a self-defensive measure, the attack can be taken to all military personnel and all military commands of the United States in the world".
He also called on the Security Council to investigate the United States' own nuclear programme.
"We insist that the responsibility of the US must be discussed too," he said.
North Korea has long been thought to have a missile under development capable of hitting the western United States.
'Chronic offender'
The International Atomic Energy Agency (IAEA) decision on Wednesday to refer North Korea to the UN Security Council brings the nuclear crisis to a new stage, our correspondent says.
CRISIS CHRONOLOGY
It raises the possibility of economic and political sanctions against Pyongyang - a move North Korea says it would regard as a declaration of war.
Under its charter, the IAEA must report any violations of the nuclear non-proliferation treaty to the Security Council, and Pyongyang had been in "chronic non-compliance since 1993", IAEA chief Mohamed ElBaradei said.
He said North Korea was only a "month or two" from producing "a significant amount of plutonium" that could be used to make nuclear weapons.
Despite issuing the referral, Mr ElBaradei insisted that the IAEA would continue to press for a peaceful solution to the crisis.
"All members made it clear it is not the time to jump to sanctions," Mr ElBaradei said.
'Window of opportunity'
Pyongyang's neighbours have reacted with concern to the new developments.
South Korea urged Pyongyang to seize the "window of opportunity" left open to it.
It also said it hoped the Security Council would "handle the issue in a way that prevents a worsening of the situation and facilitates a diplomatic resolution".
China, while backing the decision by the IAEA's 35-country board, warned the Security Council against getting involved.
"The UN Security Council's involvement at this stage might not necessarily contribute to the settlement of the issue," China's ambassador to the UN, Zhang Yan, said on Thursday.
"The only correct and effective approach... is through constructive dialogue and consultations on the basis of equality," he said.