North Korea has proposed holding a joint inquiry with the US into the hacking of Sony Pictures, claiming it can prove it did not carry out the cyber-attack.

The foreign ministry in Pyongyang denied responsibility for the the highest-profile corporate hack in history, and said there would be grave consequences if Washington refused to collaborate on an investigation and continued to blame it.

The state KCNA news agency added that claims North Korea had conducted the attack on Sony in revenge for the controversial comedy The Interview, a multimillion-dollar comedy starring James Franco and Seth Rogen that depicts the assassination of Kim Jong-un, were “groundless slander”.

KCNA quoted the foreign ministry as saying: “As the United States is spreading groundless allegations and slandering us, we propose a joint investigation with it into this incident.

“Without resorting to such tortures as were used by the CIA, we have means to prove that this incident has nothing to do with us.”

North Korea’s comments came after Barack Obama said Sony had made a mistake in axing the comedy, which had been due for release on Christmas Day.

Workers remove the poster for “The Interview” from a billboard in Hollywood Guardian

Speaking on Friday after the FBI pinned the blame for the cyber-attack on North Korea, Obama said: “We cannot have a society in which some dictator some place can start imposing censorship here in the United States, because if somebody is able to intimidate folks out of releasing a satirical movie, imagine what they start doing when they see a documentary that they don’t like, or news reports that they don’t like.

“Or even worse imagine if producers and distributors and others start engaging in self-censorship because they don’t want to offend the sensibilities of somebody whose sensibilities probably need to be offended.

“That’s not who we are. That’s not what America is about.”

Obama said he was sympathetic to Sony’s plight but added: “I wish they had spoken to me first.”

Sony Entertainment’s CEO, Michael Lynton, hit back, saying the company had been in touch with White House officials over the hacking before the film was pulled.

Lynton argued the comedy had been pulled because it would have been impossible to screen after major cinema groups backed out for fear of terrorist attacks.

Lynton told CNN he hoped the film would still be shown, but added no video on demand services had supported a release.

“We have not backed out. We have always had every desire to let the American public see it,” Lynton said.

On Wednesday Sony issued a statement saying it had “no further release plans” for the film and has also pulled its website and promotional material from an official YouTube channel.

The FBI has been investigating suspected links with North Korea’s Bureau 121 hacking unit since early December, and on Friday officials said a technical analysis of the malware used in the attack had been linked to other similar software “that the FBI knows North Korean actors previously developed”.

“We are deeply concerned about the destructive nature of this attack on a private sector entity and the ordinary citizens who worked there. Further, North Korea’s attack on SPE [Sony Pictures Entertainment] reaffirms that cyberthreats pose one of the gravest national security dangers to the United States,” the FBI said in a statement.

The White House had already labelled the attack a “serious national security matter”, but Obama would not be drawn on Washington’s reponse.

“We will respond, we will respond proportionally, and in a place and time that we choose. It’s not something that I will announce here today at this press conference,” he said.

Sony has been left reeling from the November attack, after thousands of confidential documents, including employee social security numbers, personal emails, unreleased films and executive pay were published online.

The hacking group Guardians of Peace (GOP) that claimed responsibility for the attack demanded Sony pull release of The Interview, which it did on Wednesday after threats invoking 9/11 were made against cinemagoers, and after major US theater groups cancelled screenings.

The decision has drawn the ire of many high-profile names in Hollywood, who have also criticised the press for publishing details from the hacked documents.

George Clooney called on Hollywood to get The Interview released in any format possible. “We cannot be told we can’t see something by Kim Jong-un, of all fucking people … we have allowed North Korea to dictate content and that is just insane,” he said in an interview with Deadline.

GOP reportedly sent Sony executives a message on Thursday evening, calling the studio’s decision to cancel the release “very wise”.

The statement was written in broken English and leaked to CNN. It continued: “Now we want you never let the movie released, distributed or leaked in any form of, for instance, DVD or piracy.

“And we want everything related to the movie, including its trailers, as well as its full version down from any website hosting them immediately.”