North Korea warned of strikes against the White House, Pentagon and “the whole US mainland”.
The communist country denies US claims it is behind cyber-attacks linked to The Interview movie that features the fictional killing of its leader Kim Jong-un.
North Korea has a long history of issuing threats against the US.
The latest statement comes days after the US formally accused North Korea of orchestrating a massive cyber attack on Sony Pictures.
“The army and people of the DPRK [North Korea] are fully ready to stand in confrontation with the US in all war spaces including cyber warfare space,” a long statement carried by the official Korean Central News Agency said.
“Our toughest counteraction will be boldly taken against the White House, the Pentagon and the whole US mainland, the cesspool of terrorism, by far surpassing the ‘symmetric counteraction’ declared by Obama.”
It also accuses President Barack Obama of “recklessly making the rumor” that North Korea was behind the Sony attack.
The statement also said it “estimates highly the righteous action” taken by the hackers of Sony, although it is “not aware of where they are”.
The hack resulted in unreleased films and the script for the next James Bond film being leaked online.
Details of Sony finances and private emails between producers and Hollywood figures were also released.
The eventual fallout from the attack saw Sony cancel the Christmas release of The Interview, a comedy depicting the assassination of North Korean leader Kim Jong-un.
That decision followed threats made by a group that hacked into Sony’s servers and leaked sensitive information and emails.
North Korea has denied being behind the attacks, and offered to hold a joint inquiry with the US.
The US turned down the offer, and President Barack Obama said it was considering putting North Korea back on its list of terrorism sponsors, a move that further angered Pyongyang.
North Korea had been on the US list of state sponsors of terrorism for two decades until the White House removed it in 2008, as part of now-stalled negotiations relating to Pyongyang’s nuclear program.
In an interview with CNN on December 21, Barack Obama promised to respond “proportionately” to the cyber-attack.
“I’ll wait to review what the findings are,” he said, adding that he did not think the attack “was an act of war”.
The US has reportedly also asked China to curb cyber-attacks by North Korea.
China is North Korea’s close ally and is seen as the nation with the most influence over Pyongyang.
Chinese Foreign Minister Wang Yi held a telephone conversation with his US counterpart John Kerry on December 21 in which they discussed the Sony row.
Wang Yi said China was “against all forms of cyber-attacks and cyber-terrorism” but did not refer directly to North Korea.
In a statement posted on China’s foreign ministry’s website on December 22, Wang Yi said that China “opposes any country or person using infrastructure from another country to launch a cyber attack on a third-party country”.
At a later news conference, a foreign ministry spokesman said China wanted to “engage in constructive co-operation with the international community in cyber security on the basis of mutual respect and mutual trust”.
Asked to respond to claims that North Korea was using Chinese facilities for cyber-attacks, the spokesman added: “I think to arrive at any conclusion, sufficient facts and evidence are needed. China will handle the case on the basis of facts, international laws and Chinese laws.”
Correspondents say the issue of hacking is a sensitive one in China-US relations, with the two sides frequently trading accusations of cyber-espionage.
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