An attorney for the women also said they are extremely grateful for the support of family, law enforcement and the community.
The three women remain in seclusion and released their first statements since they were found on May 6 after one of them escaped and called police.
Ariel Castro is suspected of imprisoning the women inside his house for nine years or more, allowing them outside only a few moments, and raping them. A DNA test also confirmed that Castro fathered a 6-year-old girl who one of the women gave birth to in the house. The girl escaped the house with the woman.
The women, now in their 20s and 30s, vanished separately between 2002 and 2004. At the time, they were 14, 16 and 20 years old.
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Attorney Jim Wooley read statements attributed to all three women.
The woman who was the first to disappear and the last of the three released from the hospital said, "Thank you to everyone for your support and good wishes. I am healthy, happy and safe and will reach out to family, friends and supporters in good time."
And the third woman, who was the youngest of the three, said: "I am so happy to be home, and I want to thank everybody for all your prayers. I just want time now to be with my family.