Sources told Deadline that Disney is not now planning to pay the ransom, though the studio has not yet commented publicly on the situation.
The company's future theatrical release schedule includes "Pirates of the Caribbean: Dead Men Tell No Tales" this Friday and "Cars 3" on June 16.
The gist is that Disney's CEO, Bob Iger, has revealed that hackers are claiming to have access to an upcoming Disney film and will release it online unless the studio pays an undisclosed amount of bitcoins.
Disney does not have any more films on its theatrical slate until Thor: Ragnarok on November 3, Coco on November 22, and Star Wars: The Last Jedi on December 15.
According to Deadline Hollywood, Disney is now working with the Federal Bureau of Investigation and are refusing to pay the "enormous" ransom that is being demanded.
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The Israeli authorities, meanwhile, say at least 48 Israelis have been killed in attacks by Palestinians over the same period. Israel has blamed the violence on incitement by Palestinian political and religious leaders compounded on social media sites.
Sci-fi novelist Paul Tassi, who comments on technology and the internet for Forbes Magazine, said Pirates would be unlikely to suffer were it the target, since its release date is so near.
The Disney theft comes just weeks after a hacker claimed to have stolen several episodes of Netflix's "Orange Is The New Black" and release them if the streaming service didn't pay a ransom. The hackers have however threatened to release increasingly longer pieces of the movie online if they aren't paid.
It's unclear whether the two incidents are connected.
A spokesman for Disney didn't immediately respond to a request for comment.
The hacker first tried to strong-arm the post-production company but eventually targeted Netflix with ransom demands.