David Boies, a partner at the firm, defended the producer Harvey Weinstein against accusations of sexual harassment and abuse. As part of his services, he helped orchestrate a smear campaign against the alleged victims of the mogul’s sexual misconduct and hired Black Cube, a private investigations firm staffed by former Israeli intelligence agents, to undercut accusers and the journalists looking into Mr. Weinstein.

Another team member is Mr. de Becker, who has thwarted stalkers for stars like Olivia Newton-John and Cher and provided security for public figures visiting President Ronald Reagan and his family at the White House.

Mr. de Becker is also the author of “The Gift of Fear,” a 1998 book that offers advice for dealing with threats (available on Amazon in paperback for $7.19). Concerning blackmail attempts specifically, he counseled confrontation, rather than appeasement — and it seems that Mr. Bezos followed the de Becker strategy with his blog post.

“Victims often try to appease the extortionist, but these efforts just allow him to retain the underserved mantle of a decent person,” Mr. de Becker wrote. “I suggest that clients compel the extortionist to commit to his sleaziness, which puts him on the defensive.”

In fighting back, Mr. Bezos is showing himself to be not unlike his no-holds-barred antagonist in the White House. And his media counteroffensive against the tabloid publisher has all the hallmarks of the opposition research campaigns that spice up election seasons.

Before and after Mr. Bezos published his revealing post on the online platform Medium, various media outlets gave significant space to competing and sometimes contradictory claims about the possible motives behind American Media’s big story. All of those theories had little to do with the idea that salacious details about the private life of a famous multibillionaire would be of interest to checkout-stand impulse buyers.

In an article late last month, The Daily Beast quoted Mr. de Becker as confirming that his team was looking into Michael Sanchez, the brother of Ms. Sanchez, as the potential leaker of private text messages The Enquirer published in its exposé. Mr. Sanchez denied it. As the piece noted, he is close with the Trump adviser and longtime provocateur Roger Stone, who has been indicted by the special counsel Robert S. Mueller III.