"In the darkest moments, each of their notes has been a source of comfort and hope, and they continue to be so in my current situation," wrote Polanski in a letter released online.
The 76-year-old Oscar winner made his first public statement since his arrest in September in a letter to French intellectual Bernard-Henri Levy, who has been been one of his strongest supporters.
The director of "Rosemary's Baby" and "The Pianist" is living under house arrest at his chalet in the Swiss Alpine resort of Gstaad after being released on bail on December 4.
Swiss authorities have said a decision on his extradition to the United States is expected in January.
"I have been overwhelmed by the number of messages of support and sympathy I have received in Winterthur prison, and that I continue to receive here, in my chalet in Gstaad, where I am spending the holidays with my wife and my children," Polanski wrote.
"These messages have come from my neighbours, from people all over Switzerland, and from beyond Switzerland -- from across the world."
The United States wants Polanski to face justice after he fled California in 1978 just before he was to be sentenced for having unlawful sex with a 13-year-old girl.
Polanski had pleaded guilty to the charge as part of an agreement.
In his message posted on the website of Levy's magazine Le Regle du Jeu, Polanski did not address his legal problems directly, but instead stressed that he had enjoyed much support throughout the past months.
"I would like every one of them to know how heartening it is, when one is locked up in a cell, to hear this murmur of human voices and of solidarity in the morning mail," he wrote.
"I would like to be able to answer all of them. But it is impossible: there are too many."
Polanski went on to ask Levy how best to reach out to his supporters, suggesting perhaps a text in Levy's magazine.
"Perhaps you could disseminate these few words Im sending you? I dont know. Ill leave it up to you," he added.
The Paris-born filmmaker was arrested in Switzerland on September 26 after flying in to receive an award at the Zurich film festival.
Levy has taken the lead in France to rally support for Polanski, launching an online petition calling on Swiss authorities to release this "genius filmmaker" and not allow him to be a "martyr" of a politically driven process.
French actress Isabelle Adjani and Czech author Milan Kundera are among the signatories but Levy himself has acknowledged that few leading cultural figures have signed on.
The respected author and commentator has said that Polanski is the victim of a "harassment campaign" by US judges bent on making an example of the celebrity director.
Polanski is married to French actress Emmanuelle Seigner and the couple have two children.