Bezos' request is likely in response to comments made by his security chief, Gavin de Becker, who previously told the Daily Beast that "strong leads point to political motives" in AMI's coverage.

"American Media believes fervently that it acted lawfully in the reporting of the story of Mr. Bezos," it said in a statement. "Further, at the time of the recent allegations made by Mr. Bezos, it was in good faith negotiations to resolve all matters with him. 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."

AMI insisted on Friday that it did nothing illegal but would investigate further.

In the blog post published Thursday, Bezos CEO accused AMI, the tabloid's publisher, of blackmail and extortion. He claimed that AMI asked him to publicly deny any political motivation in its coverage of his divorce.

In a blog headlined "No thank you, Mr. Pecker," Jeff Bezos claims David Pecker's National Enquirer threatened to post sexual pictures that the billionaire Amazon CEO had texted to his mistress, Lauren Sanchez, including a "below the belt selfie."

"In the AMI letters I'm making public, you will see the precise details of their extortionate proposal: They will publish the personal photos unless Gavin de Becker and I make the specific false public statement to the press that we 'have no knowledge or basis for suggesting that AMI's coverage was politically motivated or influenced by political forces,'" Bezos wrote in the post.

Bezos and his wife, MacKenzie, announced their divorce on Jan. 9. Later that day, the Enquirer broke news about Bezos' affair with Sanchez, with private photos of the two dating. Bezos never publicly addressed the Enquirer's story until Thursday.

The Enquirer is published by Pecker, who has been friends with Trump for years. Trump has often attacked Bezos, who also owns The Washington Post, which the president believes treats him unfairly.

In August, media reports said federal prosecutors gave Pecker immunity as part of an investigation into a hush-money scheme involving Trump's former personal lawyer and fixer, Michael Cohen, to keep a porn star and a former Playboy model quiet about their alleged affairs with Trump. The model, Karen McDougal, sold AMI the rights to her story about her alleged tryst, but in a practice known as "catch and kill," the publisher never ran her account. The porn star, Stormy Daniels, filed a lawsuit against Trump on March 6 to void a nondisclosure agreement she signed in October 2016 — weeks before Trump was elected president — for which she received $150,000.

Cohen has pleaded guilty to campaign-finance charges related to the payments to the women. In December prosecutors gave AMI itself immunity in the hush-money probe. As part of the agreement, the company agreed it "shall commit no crimes whatsoever." If it turns out that Bezos' blackmail allegations are confirmed, AMI could lose its immunity. Federal prosecutors in New York declined CNBC's request for comment on Bezos' accusations against AMI.

At the White House, spokesman Hogan Gidley told reporters Friday he's "not sure" if Trump is aware of the dispute between AMI and Bezos. "We're not going to get into a conversation between Jeff Bezos and a tabloid magazine," Gidley added.

In his blog post, Bezos accused AMI of "weaponizing journalistic privileges."

"These communications cement AMI's long-earned reputation for weaponizing journalistic privileges, hiding behind important protections, and ignoring the tenets and purpose of true journalism. 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. I prefer to stand up, roll this log over, and see what crawls out," Bezos wrote.

AMI did not immediately respond to CNBC's request for comment. Amazon's representative wasn't immediately available for comment.

Amazon shares were down 2 percent in early trading Friday.

Here is the copy of the email Bezos received from AMI, according to his blog post. CNBC and NBC News have not independently reviewed the emails.

From: Howard, Dylan [XXXXX@XXXXX] (Chief Content Officer, AMI)

Sent: Tuesday, February 5, 2019 3:33 PM

To: Martin Singer (litigation counsel for Mr. de Becker)

Subject:. Jeff Bezos & Ms. Lauren Sanchez Photos

CONFIDENTIAL & NOT FOR DISTRIBIUTION

Marty:

I am leaving the office for the night. I will be available on my cell — 917 XXX-XXXX.

However, in the interests of expediating this situation, and with The Washington Post poised to publish unsubstantiated rumors of The National Enquirer's initial report, I wanted to describe to you the photos obtained during our newsgathering.

In addition to the "below the belt selfie — otherwise colloquially known as a 'd*ck pick'" — The Enquirer obtained a further nine images. These include:

· Mr. Bezos face selfie at what appears to be a business meeting.

· Ms. Sanchez response — a photograph of her smoking a cigar in what appears to be a simulated oral sex scene.

· A shirtless Mr. Bezos holding his phone in his left hand — while wearing his wedding ring. He's wearing either tight black cargo pants or shorts — and his semi-erect manhood is penetrating the zipper of said garment.

· A full-length body selfie of Mr. Bezos wearing just a pair of tight black boxer-briefs or trunks, with his phone in his left hand — while wearing his wedding ring.

· A selfie of Mr. Bezos fully clothed.

· A full-length scantily-clad body shot with short trunks.

· A naked selfie in a bathroom — while wearing his wedding ring. Mr. Bezos is wearing nothing but a white towel — and the top of his pubic region can be seen.

· Ms. Sanchez wearing a plunging red neckline dress revealing her cleavage and a glimpse of her nether region.

· Ms. Sanchez wearing a two-piece red bikini with gold detail dress revealing her cleavage.

It would give no editor pleasure to send this email. I hope common sense can prevail — and quickly.

Dylan.