(Photo: AP)

The publisher of the National Enquirer says it will investigate Amazon CEO Jeff Bezos’ allegation that it threatened to publish revealing personal photos of him unless he stopped investigating how the tabloid obtained his private exchanges with his mistress.

American Media Inc. says in a statement issued Friday it “acted lawfully” while reporting the story.

The Enquirer published a story last month that included lurid texts between Bezos and former TV anchor Lauren Sanchez. Since then, private investigators have been looking into how the Enquirer got the texts.

Bezos says he was the target of “extortion and blackmail” by American Media. But the company says it engaged in “good faith negotiations.”

American Media says its board of directors ordered a prompt and thorough investigation. It says it’ll take “whatever appropriate action is necessary.”

Amazon CEO Jeff Bezos says he was the target of “extortion and blackmail” by the publisher of the National Enquirer. He says the Enquirer chief threatened to publish revealing personal photos of Bezos unless he stopped investigating how the tabloid obtained his private exchanges with his mistress.

Bezos, who is also owner of The Washington Post, detailed his interactions with American Media Inc., in an extraordinary blog post Thursday on Medium.com. The billionaire said the Enquirer wanted him to make a public statement that the tabloid’s coverage was not politically motivated.

Bezos’ accusations add another twist to a high-profile clash between the world’s richest man and the leader of America’s best-known tabloid.