Bezos says that the Enquirer is threatening to publish even more embarrassing photos of him if he doesn't put a stop to an investigation now underway by a private investigator hired by Bezos.
As far as why the outlet would go to such lengths, with threats to release "below the belt selfie", among other images, Bezos cited his lawyer's investigation into how National Enquirer obtained the texts, as well as Pecker's reported actions on behalf of President Donald Trump and on behalf of the Saudi Government.
According to the letters, in exchange for not publishing these photos, AMI's Deputy General Counsel, Jon Fine, wanted Bezos and his team to acknowledge that "they have no knowledge or basis for suggesting that AMI's coverage was politically motivated or influenced by political forces, and an agreement that they will cease referring to such a possibility".
But as Bezos began to investigate the leak, the tabloid's parent disputed any suggestion that its story was politically motivated. "Of course I don't want personal photos published, but I also won't participate in their well-known practice of blackmail, political favors, political attacks, and corruption". A representative for AMI responded in one of the emails: "With millions of Americans having a vested interest in the success of Amazon, of which your client remains founder, chairman, CEO, and president, an exploration of Mr. Bezos' judgment as reflected by his texts and photos is indeed newsworthy and in the public interest".
A spokesman for the USA attorney's office in Manhattan did not immediately comment on Bezos' assertion that AMI had committed extortion. Mr Bezos owns The Washington Post, which has relentlessly reported on the murder past year of its columnist Jamal Khashoggi, a Saudi dissident.
Mr Bezos and his wife, MacKenzie, said last month they were getting divorced. Do you see how much I like writing "Pecker"? The Enquirer secured the rights to the material, assuring the allegations wouldn't be shared with other media, then never published the story.
In an extraordinarily personal online post, Mr Bezos said intermediaries of Mr David Pecker, chairman of American Media Inc (AMI), the owner of The Enquirer, had approached him to stop his investigation. He owns the Washington Post, which has written critical stories about Trump, who counts Pecker as a close ally.
Those who support the president may have been motivated to move against Mr Bezos since Mr Trump has long criticised the billionaire.
That admission was part of a deal between AMI and federal prosecutors, who agreed to not pursue charges against the company for secretly assisting Trump's campaign by paying $150,000 U.S. to a Playboy model for the rights to her story about an alleged affair with the then-candidate.
Instead, Bezos published emails from Enquirer executives to a lawyer representing de Becker, including one in which top editor Dylan Howard appears to suggest that the Enquirer would publish revealing photos of Bezos and Sanchez.