Amanda Berry, Gina DeJesus and Michelle Knight issued a statement through a public relations firm, The (Cleveland) Plain Dealer reported. The letter also thanked the news media for respecting the women's desire for privacy.
The letter said $650,000 has been donated to the Cleveland Courage Funds.
"These three brave women have asked us to give this message to everyone who has expressed concern and support," the letter from Hennes Paynter Communications said. "Amanda, Gina and Michelle want you to know they are doing well. They are happy and safe and continue to heal, a process that requires time and privacy."
Ariel Castro, 52, allegedly abducted the women from his Cleveland neighborhood and kept them prisoner for more than a decade, raping them repeatedly. He is being held on $8 million bail.
The women were discovered earlier this month when Berry attracted the attention of two neighbors and came out of the house with her 6-year-old daughter.