American Media has launched an investigation into extortion claims made by Jeff Bezos after the billionaire entrepreneur published exchanges between his team and the media company in a revealing Medium post.

In a statement responding to the allegations, American Media said it “believes fervently that it acted lawfully in the reporting of the story of Mr Bezos” but “nonetheless, in light of the nature of the allegations published by Mr Bezos, the board has convened and determined that it should promptly and thoroughly investigate the claims”.

“Upon completion of that investigation, the board will take whatever appropriate action is necessary,” the statement continued.

The investigation follows claims Mr Bezos made on Thursday, alleging he was the target of “extortion and blackmail” by the publisher of the National Enquirer, which he said threatened to publish revealing personal photos of him unless he stopped investigating how the tabloid obtained his private exchanges with his mistress.

In detailing his interactions with American Media, or AMI, Mr Bezos – who is also the owner of The Washington Post, said the tabloid wasn’t seeking money, but rather wanted him to make a public statement claiming the Enquirer’s coverage was not politically motivated.

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The accusations add another twist to a high-profile clash between the world’s richest man and the leader of America’s best-known tabloid, a strong backer of Donald Trump. Mr Bezos’s investigators have suggested the Enquirer’s coverage of his affair – which included the release of risque texts – was driven by dirty politics.

“Of course I don’t want personal photos published, but I also won’t participate in their well-known practice of blackmail, political favours, political attacks, and corruption,” he wrote of AMI, in explaining his decision to go public. “I prefer to stand up, roll this log over, and see what crawls out.”

The company has admitted in the past that it engaged in what’s known as “catch-and-kill” practices to help Mr Trump become president. The president has been highly critical of Mr Bezos and The Post’s coverage of the White House.

The Bezos affair became public when the Enquirer published a story in January about his relationship with Lauren Sanchez, a former TV anchor who is also married. Mr Bezos then hired a team of private investigators to find out how the tabloid got the texts and photos the two exchanged.

Several days ago, someone at AMI told Mr Bezos’s team that the company’s chief executive David Pecker was “apoplectic” about the investigation, he said. AMI later approached Mr Bezos’s representatives with an offer.

“They said they had more of my text messages and photos that they would publish if we didn’t stop our investigation,” he wrote.

Mr Bezos wrote that this week, the tabloid’s editor, Dylan Howard, emailed an attorney for Bezos’s longtime security consultant to describe photos the Enquirer “obtained during our newsgathering”. The photos include a “below the belt selfie” of the Amazon CEO, photos of him in tight boxer-briefs and wearing only a towel, and several revealing photos of Ms Sanchez, according to the emails he released.

According to the emails, an attorney for AMI offered a formal deal Wednesday. The tabloid wouldn’t post the photos if Mr Bezos and his investigators would release a public statement “affirming that they have no knowledge or basis” to suggest the Enquirer’s coverage was “politically motivated or influenced by political forces”.

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Mr Bezos said he decided to publish the emails sent to his team “rather than capitulate to extortion and blackmail”, despite the “personal cost and embarrassment they threaten”.