The 76-year-old is currently under house arrest in his chalet in Gstaad, with bail set at €3m (£2.5m). He is wanted by US authorities for fleeing trial in 1978, after having plead guilty to unlawful sex with a 13-year-old girl and spending 42 days in a Californian prison.
The letter, entitled 'I Can Remain Silent no Longer', is being circulated in France by his friend, the philosopher Bernard-Henri Lévy, according to The Guardian.
Polanksi claims that he has served his sentence and that he was betrayed by the judge in his case - meaning that he was "justified" in fleeing.
"That period was to have covered the totality of my sentence," he writes. "By the time I left prison, the judge had changed his mind and claimed that the time served at Chino did not fulfil [sic] the entire sentence, and it is this reversal that justified my leaving the United States."
He adds: "The judge decided to repudiate [Polanski's plea bargain agreement] in order to gain himself some publicity at my expense."
Polanski said that the US wanted his extradition to "serve me on a platter to the media" and added that he had had to mortgage his apartment to raise bail.