A former member of the Navy SEALs who wrote a best seller about the raid that killed Osama bin Laden is under criminal investigation for possibly disclosing classified material, according to federal officials and his lawyer.

The lawyer for the former SEALs member, Matt Bissonnette, said the investigation was focused on whether Mr. Bissonnette had disclosed classified information in the book “No Easy Day,” published under a pseudonym in 2012. But other people familiar with the inquiry said investigators seemed more interested in paid speeches that Mr. Bissonnette, who says he was one of the members of the Navy’s SEAL Team 6 who shot Bin Laden, gave at corporate events.

They include at least one talk last year, at a golf club in Atlanta, in which audience members were asked to turn in their cellphones before he spoke so that nothing could be recorded, according to people who attended the event.

Mr. Bissonnette has apologized for failing to have the book vetted through the Pentagon’s required security review process.