The hackers, calling themselves the Guardians of Peace, warned Tuesday that the worst is yet to come.
In a statement, they said: "We will clearly show it to you at the very time and places 'The Interview' be shown, including the premiere, how bitter fate those who seek fun in terror should be doomed to."
Their statement said the move was "awful" and promised "the world will be full of fear."
After referencing the 9/11 terrorist attacks, the group said people should stay away from "The Interview," which is scheduled to premier Christmas Day.
In a statement, the FBI said it is "aware of recent threats and continues to work collaboratively with our partners to investigate the Sony attack."
The Department of Homeland Security said there is no credible intelligence that any active plot exists, but that along with the FBI, it is still analyzing hack and the "credibility" of the threats. Private security firms are also involved in the technical investigation.
"The Interview" is a comedy in which Seth Rogen and James Franco star as television journalists involved in a CIA plot to assassinate North Korean leader Kim Jong Un. Its New York premiere is scheduled for Thursday at Manhattan's Landmark Sunshine. It premiered in Los Angeles last week.
The hackers said: "All the world will denounce the SONY."
Patrick Corcoran, spokeman for the National Association of Theater Owners, wouldn't comment on the threats.
Highly sensitive material from the entertainment unit of Tokyo-based Sony Corp. has been leaked almost daily since the hackers broke into its computer networks last month.
One the same day of the latest threat from the hackers, news emerged that two former employees of Sony Pictures Entertainment are suing the company for not preventing the cyberattack.
They say the company should have done more to stop the hackers from stealing nearly 50,000 social security numbers, salary details and other personal information from current and former workers.
The federal suit alleges that emails and other information leaked by the hackers show that Sony's information-technology department and its top lawyer believed its security system was vulnerable to attack, but that company did not act on those warnings. The plaintiffs are asking for compensation for fixing credit reports, monitoring bank account and other costs as well as damages.
The suit filed Tuesday in U.S. district court in California seeks class-action status.
Sources tell CBS News the cyberattack on Sony Pictures used an especially aggressive malware capable of erasing hard drives and crashing computer networks.
The personal information of more than 6,000 Sony employees, and four unreleased Sony films were posted to the Internet.
Now investigators are wondering if the attack might be retaliation for "The Interview," because of the plot focused around assassinating Kim Jong-un.
Investigators wonder if the plot of that movie may have triggered retaliation against Sony. Sources say the malware code is written in Korean, and North Korean hackers have used a similar cyber weapon before in a 2013 attack on banks and broadcasters in South Korea.
North Korea has denied it was behind the hack, but did praise the cyberattack as a "righteous deed."
In a statement, Pyongyang criticized the film for "abetting a terrorist act while hurting the dignity of the supreme leadership."