Assange, 42, who has been holed up in the Ecuadorian Embassy in London for more than a year to avoid extradition to the United States - refused the request to meet as Cumberbatch prepared for his role in The Fifth Estate.
Despite Assange railing against the film, two days before it hits cinema screens he has released a letter he wrote to the actor on his website.
Assange claims the Dreamworks production is based on a "toxic" book and believes the film "will distort events and subtract from public understanding" of his work.
Assange told the 37-year-old English actor: "I believe you are a good person, but I do not believe that this film is a good film. I do not believe it is going to be positive for me or the people I care about."