The Australian hacker, who has been holed up at the Ecuadoran embassy in London after claiming asylum a year ago to avoid extradition to Sweden, has refused to meet the British actor.
Cumberbatch stars as Assange in director Bill Condon's thriller "The Fifth Estate," which won a long ovation at its world premiere during the Toronto Film Festival last month and is due for release in the United States next week.
"I believe you are a good person, but I do not believe that this film is a good film," said Assange's letter to the actor, who revealed last month he considered quitting the movie after receiving it.
"Feature films are the most powerful and insidious shapers of public perception, because they fly under the radar of conscious exclusion," said the letter.
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"This film is going to bury good people doing good work, at exactly the time that the state is coming down on their heads. It is going to smother the truthful version of events, at a time when the truth is most in demand.
In comments accompanying the release of the letter, he added: "The result is a geriatric snoozefest that only the US government could love."
According to Assange, Cumberbatch's reply was "courteous and considered" with the actor admitting aspects of the script troubled him.
The letter exchange took place in January.
At the Toronto Film Festival, Cumberbatch, who has won rave reviews, said he wanted to see Assange carry on his work exposing secrets.
WikiLeaks enraged the United States in 2010 by publishing hundreds of thousands of classified documents on the wars in Iraq and Afghanistan, as well as a huge cache of US diplomatic cables that embarrassed governments worldwide.
Ecuador granted Assange asylum last year but Britain refuses to grant him safe passage out of the country, leaving him stuck inside the embassy.
Britain says it is obliged to see him extradited to Sweden where he faces sex crime allegations that Assange denies and claims are politically motivated.