Obama said during a press conference Friday that Sony "made a mistake" in dropping "The Interview."
However, the studio fired back, saying the cancellation happened only because the country's top theatre chains pulled out.
"This was their decision," Sony said in a statement.
Sony insists it has only cancelled the Christmas Day release and that it has been "actively surveying alternatives" to release the film on a different platform.
In an interview with CNN Friday, Sony Pictures Entertainment CEO Michael Lynton said "the President, the press and the public are mistaken about what happened."