She says she respects Mr Petraeus' privacy and wants the same for her own family.
Petraeus resigned on Friday after admitting to an extramarital affair with his biographer, Paula Broadwell.
The FBI learned of the affair as it was investigating emails sent by Mrs Broadwell to Ms Kelley, who serves as an unpaid social liaison to MacDill Air Force Base in Tampa.
Ms Kelley issued the statement through Smith and Company, a Washington communications and crisis management firm.
Mrs Broadwell told Ms Kelley to 'stay away from my guy' after believing he had found a new lover.
The New York Post reports excerpts from the emails that Ms Kelley passed on to the FBI with sources telling the newspaper that 'Mrs Broadwell clearly thought something was going on' and thought she was in a 'lovers triangle.'
She told Ms Kelley 'I know what you did' and warned her to 'back off.'
The Washington Post reports that Ms Kelley was so scared she called the FBI who were concerned that the CIA director's personal e-mail account had been hacked and that national security had been threatened.
But after interviews with Mr Petraeus and Mrs Broadwell it was discovered that Mr Petraeus, one of America's most decorated soldiers and its spy boss was secretly having an affair with the pretty biographer and married mum of two.
In an email from Mr Petraeus to a longtime friend and obtained by the Washington Post, he expressed regret for letting down his family and the nation.
"He was deeply sorry for the pain he has caused his family," the friend said.
"He also noted how much he loved his job at the agency. He said he really relished the intellectual challenge there."
The love tryst, which began in the battlefields of Afghanistan, was only uncovered after the FBI launched an investigation into Mrs Broadwell for allegedly hacking into the general's email as part of an abusive attack on Kelley.
While in his account, the FBI discovered sexually explicit emails between Mr Petraeus and Mrs Broadwell - reportedly including one which made references to engaging in sex under a desk.
Other reports suggest Mrs Broadwell split from Mr Petraeus in 2011, and that the general continued to pursue her with hundreds of emails during the past year.
The FBI brought the matter up with Mr Petraeus directly after being alerted that Mrs Broadwell may have had access to his personal email account. The emails involved in the matter were in most instances sent from the personal account, not his CIA one.
As the general was married and had the nations' highest security clearance, the affair was deemed a national security risk and investigated further as it potentially exposed the CIA head to blackmail.
The retired four-star general was a leading commander in both the Iraq and Afghanistan wars following 9/11. He was credited with the counter-offensive surge strategy that tamed the Iraq insurgency.
Known as a straight shooter, he was highly regarded on both sides of the political aisle. Republicans touted him as a potential presidential candidate, while President Barack Obama made him part of his cabinet.
Mr Petraeus stepped down after he confessed to cheating on his wife of 37 years, Holly - behaviour he explained was 'unacceptable' for a senior administration official.
Members of Congress said they want answers to questions about the affair that led to Mr Petraeuss resignation.
The president will likely have to replace not only departing Secretary of State Hillary Clinton, but also Defence Secretary Leon Panetta and Treasury Secretary Tim Geithner.
One name being floated as a possible Petraeus replacement is John Brennan, the White House counter-terrorism adviser and a CIA veteran who has played an instrumental role in Obama's drone war against al-Qaeda militants.
The most celebrated military officer of his generation, Petraeus took over at the CIA a little more than a year ago.
Mrs Broadwell has not responded to multiple emails and phone messages. Mrs Broadwell planned to celebrate her 40th birthday party in Washington this weekend, with many reporters invited. But her husband emailed guests to cancel the event late Friday.
Mrs Broadwell, who lives in Charlotte, North Carolina, with her radiologist husband Dr Scott Broadwell and their two young sons Lucien and Lando, was embedded with Mr Petraeus in Afghanistan, and said the two would go on 8km jogs together.
The keen runner said she wanted to test him to see if he could keep up with her as she interviewed him.
"Instead it became a test for me,'' she said.
"As we talked during the run from the Pentagon to the Washington Monument and back, Petraeus progressively increased the pace until the talk turned to heavy breathing and we reached a six-minute-per-mile pace. It was a signature Petraeus move."