A hacker apparently accessed private photos and emails sent between members of the Bush family, including both former presidents, and the Secret Service is investigating.
The Smoking Gun website said the hacker, who went by the online moniker "Guccifer," gained access to emails, photos, private telephone numbers and addresses of Bush family members and friends.
The website displayed photos it said came from the hacker, including one that purported to show the elder Bush during his recent stay in a Houston hospital, where the 88-year-old spent almost two months being treated for complications from a bronchial infection.
The authenticity of the photos and other details on the website could not immediately be confirmed. A spokesman for former President George HW Bush declined to comment on the reports.
"There's a criminal investigation and, as such, there's nothing else we can say," Jim McGrath said Friday.
Secret Service spokesman George Ogilvie said the agency was investigating. He would not elaborate.
In Dallas, where Bush's son, former President George W Bush has a home, Bush spokesman Freddy Ford declined to make a statement.
The FBI in Houston, where the elder Bush lives, would not confirm or deny any investigation.
George HW Bush's son Jeb Bush, the former governor of Florida, when reached by email, said the hacking was "outrageous" and the decision to publish the material showed "total disregard for privacy".
The word "Guccifer" was plastered across the photos published on the website, which quotes "Guccifer" as describing himself as a veteran hacker who has long been in the government's sights.
Free email accounts from commercial providers are especially vulnerable to hackers who exploit easy-to-use features to reset email passwords. AOL's email passwords can be reset by a hacker who could discover, for example, the birth year of a customer's mother, a father's middle name or the name of a favourite pet.
Last year, after The Associated Press revealed that Republican presidential candidate Mitt Romney and some top aides had used private email accounts to conduct state business at times when Romney was governor of Massachusetts, Romney's free Microsoft Hotmail account was hacked.
The alleged hacker claimed to have guessed the answer to a security question about Romney's favourite pet in order to gain access to the account and change the password. The anonymous hacker said Romney's account on DropBox, a file-sharing service, also was compromised.
A college student in Tennessee, David Kernell, was convicted in April 2010 on federal charges of hacking into Sarah Palin's private emails weeks before the 2008 presidential election. Kernell had correctly guessed answers to security questions guarding Palin's account, giving him access.
Last year, a group of hackers known as the D33D Company published a list of what it said were usernames and passwords for more than 450,000 email accounts, including more than 25,000 AOL accounts. It was not immediately clear whether the Bush family's hacked AOL accounts were among these.