Mrs Kelley, 37, of Tampa, Florida, went to the FBI after receiving threatening emails that were eventually traced to the general's biographer, Paula Broadwell, in an investigation which discovered Mr Petraeus and Ms Broadwell were having an extramarital affair.
Mrs Kelley, a volunteer social liaison with military families, issued a statement saying: "We and our family have been friends with General Petraeus and his family for over five years. We respect his and his family's privacy and want the same for us and our three children."
Mr Petraeus resigned on Friday after admitting an extramarital affair with married mother-of-two Ms Broadwell. He has been married to Holly Petraeus, with whom he has two children, including a son who led an infantry platoon in Afghanistan, for 38 years.
A friend of the general, Colonel Steve Boylan, said Mr Petraeus is devastated and his wife furious.
Meanwhile, members of the US Congress are demanding more details about the FBI investigation and whether national security was compromised.