Bezos opened an investigation into the leak led by Gavin de Becker, a public safety expert, who told media there were "political motives" behind the move.
"Rather than capitulate to extortion and blackmail", Bezos said, "I've chose to publish exactly what they sent me, despite the personal cost and embarrassment they threaten".
Earlier Friday, AMI said it "acted lawfully" while reporting the story and that it engaged in "good faith negotiations" with Bezos.
"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".
AMI chief David Pecker is a friend of Trump's, and as Bezos notes, Pecker was granted immunity for his cooperation in a federal probe of Trump's payments to women who claim they had an affair with the president prior to his election.
On Thursday, Bezos wrote a post on the website Medium.com where he shared the emails AMI executives had sent him, threatening to leak his and Sanchez's photos if he didn't stop the investigation. They also included his personal text messages and pictures in the report.
The Amazon boss had hired a private investigator to look into whether AMI's revelation of his affair was "politically motivated". That investigation so panicked Mr. Pecker over at the Enquirer that his lawyer sent a confidential letter demanding that either Bezos call off that detective - or else the Enquirer would publish private photographs of Bezos and Sanchez. The headline in the Bezos-owned Washington Post says "Bezos makes extortion allegation".
Senate Leader McConnell cautions Pres. Trump about wall emergency
He questioned whether the US should have invaded Afghanistan in 2001 under the administration of former President George W. Bush to destroy al-Qaida training grounds after the terrorist group's attacks on the USA killed almost 3,000 people.
AWS representatives, presumably still dazed by this whole thing like the rest of us, did not respond to a request for comment on the breadth and depth of American Media's spending on the cloud computing giant's services. The deal not to prosecute was conditional on AMI not committing another crime, the office said.
In his blog post, Bezos wrote that he's not playing along.
"After Mr. Trump became president, he rewarded Mr. Pecker's loyalty with a White House dinner to which the media executive brought a guest with important ties to the royals in Saudi Arabia".
She added: "AMI declined to comment tonight, but there are questions here".
The agreement with NY prosecutors required AMI to commit no further crimes for at least three years, but the company's alleged threat to Bezos could be interpreted as a breach, potentially opening it to prosecution. "And we know, because we follow the news, that when AMI panics like that, about that, we know they're doing so in the context of their still-active non-prosecution agreement with the Southern District of NY (still valid until at least the fall of 2021)".
Given Pecker's longtime friendship with President Trump, the Enquirer's role in "catching and killing" stories to help Trump, and and Bezos's presence on Trump's enemies list, many commentators have speculated about a potential Trump connection in this case - but it is just speculation.
Mr Trump's former lawyer Michael Cohen - who facilitated the hush money at the direction, he says, of Mr Trump - has already admitted violating campaign finance laws. "In a tweet, he said Mr.de Becker "spreads fake, unhinged conservative conspiracy theories" and "'dog whistle' smears". Or at least that's what the top people at the National Enquirer thought.