An anonymous hacker claims to have breached the personal e-mail account of CIA Director John Brennan, seen in 2014. (Pablo Martinez Monsivais/AP)

The FBI is investigating claims by an anonymous computer hacker that he stole potentially sensitive files from the private e-mail account of CIA Director John Brennan and posted them online, U.S. officials said.

The exposed documents appear to include a roster of senior U.S. national security officials with their phone and Social Security numbers, a log of calls made by former CIA deputy director Avril Haines and a list of e-mail addresses that the hacker claimed were taken from Brennan’s AOL account.

A CIA spokesman said, “We are aware of the reports that have surfaced on social media and have referred the matter to the appropriate authorities.”

Other U.S. officials said that the FBI had launched an inquiry and that the Secret Service was investigating related claims that the hacker obtained private information from Homeland Security Secretary Jeh Johnson.

The potential breaches are likely to intensify security concerns over senior government officials’ use of private e-mail and Internet accounts. Hillary Rodham Clinton’s campaign for president has been beset by allegations that classified material may have been exposed on the private e-mail server she used while serving as secretary of state.

The claims were first reported Monday by the New York Post, which described the unnamed hacker as a “stoner high-school student” who told the newspaper that Brennan’s account was used to store sensitive files, including his 47-page application for a top-secret security clearance. It was unclear whether that application had been posted online.

The hacker said he was motivated by “opposition to U.S. foreign policy and support to Palestine.”

He said he had obtained the information through a “social engineering” ploy in which he posed as a Verizon technician and tricked the company’s tech-
support unit into revealing Brennan’s account number, password and other details. He said he then used that information to pose as Brennan in a call to AOL in which he requested a reset of the CIA chief’s online password.

The hacker said he had repeatedly prank-called Brennan since August, once reading the CIA director’s Social Security number to him over the phone before Brennan hung up.

The New York Post reported that the hacker’s access was cut off after Brennan learned that his account had been infiltrated. Some of the files appear to predate Brennan’s tenure as CIA director. ­Before taking that job in 2013, he served as President Obama’s top counterterrorism adviser.

The hacker also claimed to have broken into the Comcast account of Johnson and listened to his voice mails and taken a screen shot of a billing page.

Previous CIA directors have faced serious consequences for computer-related breaches. John Deutch was stripped of his security clearances in 1999 after mishandling classified information on home computers. And David H. Petraeus resigned from the top CIA post in 2012 after admitting to an extramarital affair that FBI investigators had uncovered in his personal e-mails.

Ellen Nakashima and Julie Tate contributed to this report.