In its first substantive response to the accusation,the isolated North Korea said it could prove it had nothing to do with the massive hacking attack.
"We propose to conduct a joint investigation with the U.S. in response to groundless slander being perpetrated by the U.S. by mobilizing public opinion," the North Korean spokesman said.
"If the U.S. refuses to accept our proposal for a joint investigation and continues to talk about some kind of response by dragging us into the case, it must remember there will be grave consequences," the spokesman said.
Earlier, the U.S. Federal Bureau of Investigation announced it had determined that North Korea was behind the hacking of Sony, saying Pyongyang's actions fell "outside the bounds of acceptable state behavior".
Obama said North Korea appeared to have acted alone. Washington began consultations with Japan, China, South Korea and Russia seeking their assistance in reining in North Korea.
Japan and South Korea said they would cooperate. China, North Korea's only major ally, has yet to respond, but a Beijing-run newspaper said "The Interview" was not a movie for Hollywood and U.S. society to be proud of.
"The vicious mocking of Kim is only a result of senseless cultural arrogance," the newspaper said.
It was the first time the United States had directly accused another country of a cyberattack of such magnitude on American soil and set up a possible new confrontation between longtime foes Washington and Pyongyang.
Obama said he wished that Sony had spoken to him first before yanking the movie,suggesting it could set a bad precedent. "I think they made a mistake," he said.
Sony Pictures Entertainment Chief Executive Michael Lynton insisted the company did not capitulate to hackersand said it is still looking for alternative platforms to release "The Interview." This week, a spokeswoman for Sony had said the company did not have further release plans for the $44 million film starring Seth Rogen and James Franco.
Despite Obama's stern warning to North Korea, his options for responding to the computer attack by the impoverished state appeared limited. The president declined to be specific about any actions under consideration.
North Korea has been subject to U.S. sanctions for more than 50 years, but they have had little effect on its human rights policies or its development of nuclear weapons. It has become expert in hiding its often criminal money-raising activities, largely avoiding traditional banks.
The FBI said technical analysis of malicious software used in the Sony attack found links to malware that "North Korean actors" had developed and found a "significant overlap" with "other malicious cyber activity" previously tied to Pyongyang.
But it otherwise gave scant details on how it concluded that North Korea was behind the attack.
U.S. experts say Obama's options could include cyber retaliation, financial sanctions, criminal indictments against individuals implicated in the attack or even a boost in U.S. military support to South Korea, still technically at war with the North.
But the effect of any response would be limited given North Korea's isolation and the fact that it is already heavily sanctioned for its nuclear program.
There is also the risk that an overly harsh U.S. response could provoke Pyongyang to escalate any cyber warfare.
Non-conventional capabilities such as cyber warfare and nuclear technology are the weapons of choice for the impoverished North, defectors said in Seoul.
They said the Sony attack may have been a practice run for North Korea's "cyberarmy" as part of its long-term goal of being able to cripple its rivals' telecommunications and energy grids.
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