LOS ANGELES  Ending a long silence, Roman Polanski addressed his possible extradition to the United States over a 33-year-old sex-crime case with a statement that accused authorities here of “trying to serve me on a platter to the media of the world,” instead of honoring what he described as an agreement, made decades ago, to limit his punishment to time already served.

“I have decided to break my silence in order to address myself directly to you without any intermediaries and in my own words,” Mr. Polanski said in the statement, which was distributed to the news media on Sunday.

The 908-word statement was circulated by Bernard-Henri Lévy, who is a friend of Mr. Polanski’s and the director of the French magazine La Règle du Jeu. Mr. Polanski, the Oscar-winning director whose films include “The Pianist” and “Chinatown,” was arrested in Switzerland on Sept. 26. He has since been held pending possible extradition for sentencing in the case that stemmed from his arrest in 1977 after having sex with a 13-year-old girl.