In a statement on her MySpace page, the Oscar-winning actress and singer says: "I want to thank each and every one of you for your thoughts and prayers during this difficult time. My sister and I take great comfort and strength from your love and concern."
Last week, Hudson buried her mother, brother and 7-year-old nephew, who were all slain in her hometown of Chicago. Hudson has been in seclusion since the tragedy.
Meanwhile, the Gap is unveiling new ads featuring a smiling Hudson. However, her representative says the campaign went to print before the tragedies.