Its foreign ministry accused the US of "spreading groundless allegations", which a joint inquiry would refute.
Without addressing Pyongyang's idea, a US spokesman insisted North Korea must admit "culpability" .
Sony has cancelled the release of The Interview, which includes plans to kill the fictional Kim Jong-un.
The Interview had been due to open on Christmas Day. However, after anonymous threats against cinemas, Sony said it was considering releasing it "on a different platform".
The FBI said on Friday that North Korea had carried out last month's cyber-attack, in which script details and private emails were leaked.
The US defended its findings on Saturday, saying it was confident the North Korean government was "responsible for this destructive attack".
"If the North Korean government wants to help, they can admit their culpability and compensate Sony for the damages this attack caused," US National Security spokesman Mark Stroh said.Dire warning
On Saturday, the North Korean foreign ministry said: "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 US CIA, we have means to prove that this incident has nothing to do with us."
The statement said there would be "grave consequences" if the Americans rejected their inquiry proposal.The film had been scheduled for release on 25 December North Korea says the film hurts the "dignity of its supreme leadership" Steve Evans, BBC News, Seoul
The denial by North Korea is unlikely to convince everyone. Defectors from the North said there was a unit of the military there called Bureau 121 which hacks the websites of foreign organisations.
In March last year hackers calling themselves the Dark Seoul Gang attacked the systems of South Korean banks and television stations. Experts say the methods were similar to the attack on Sony Pictures.
North Korea is an isolated country developing nuclear weapons and ruled by a despot so the increased irritation in Pyongyang on top of Sony's apparently new intention to release the controversial film, perhaps on the web, is causing heightened anxiety in the region.
On Friday US President Barack Obama criticised the cancellation, saying he wished Sony executives had spoken to him before cancelling the release.
"We cannot have a society in which some dictator someplace can start imposing censorship," he said, vowing to "respond" to the cyber-attack in a "manner that we choose".
Responding to the US president's comments, Sony Pictures chief executive and chairman Michael Lynton said the studio had not made an error in cancelling the release.
"We have not given in, we have persevered," he told CNN.
A Sony statement said the decision had been based on "the majority of the nation's theatre owners choosing not to screen the film".
"Without theatres, we could not release it in the theatres on Christmas Day. We had no choice," the statement added.
"It is still our hope that anyone who wants to see this movie will get the opportunity to do so."
The movie features James Franco and Seth Rogen as two journalists who are granted an audience with Mr Kim.
The CIA then enlists the pair to assassinate him.
The film's cancelled release drew criticism in Hollywood, with some calling it an attack on the freedom of expression.
Actor George Clooney told the trade website Deadline on Thursday the film should be released online, saying Hollywood should not be threatened by North Korea.