North Korea said on Saturday that U.S. accusations indicating it was involved in a cyberattack on Sony Pictures were "groundless slander" and warned of "serious consequences" for any possible retaliation against it. But at the same time, the isolated nation offered to prove its innocence by proposing a joint investigation into the incident with Washington—a move that Pyongyang knows the U.S. is not likely to take seriously.

The statement, which was attributed to an unnamed Foreign Ministry spokesperson and carried by North Korea's official KCNA news agency, is in response to President Obama's statement on Friday that blamed North Korea for the hacking and the suggestion that the U.S. would retaliate.

"We have a way to prove that we have nothing to do with the case without resorting to torture, as what the CIA does," said the spokesman, adding the warning that, "The U.S. should bear in mind that it will face serious consequences in case it rejects our proposal for joint investigation and presses for what it called countermeasures."

On Friday, President Barack Obama blamed North Korea for the cyberattack, which has caused significant embarrassment for Sony and led to the Hollywood studio canceling "The Interview," a satirical film centered around the plot of a fictional assassination of North Korean leader Kim Jong Un. During his statement, Obama said that the U.S. "will respond proportionally" and "in a place and time and manner that we choose." But North Korea suggested that an escalation in American accusations would have "grave consequences" of their own.