In his blog post on Thursday, Mr Bezos said he chose to publish the emails sent to his team "rather than capitulate to extortion and blackmail", despite the "personal cost and embarrassment they threaten".
It said the company believed "fervently that it acted lawfully in the reporting of the story of Mr Bezos".
In recent months, the Trump-friendly tabloid acknowledged secretly assisting Mr Trump's White House campaign by paying Ms McDougal for the rights to her story about the alleged affair.
Trump's longtime personal attorney and fixer Michael Cohen pleaded guilty past year to charges that included helping to broker that transaction.
Media captionWas Trump's Stormy Daniels payment legal? AMI also allegedly enteredinto an immunity deal with the Department of Justice about the "catch and kill" process.
The simple fact of the matter is that any statements AMI made admitting a role in the scheme Cohen already pleaded guilty to can and will backfire if the investigation of the Bezos situation voids the non-prosecution deal.
Prosecutors in the Manhattan U.S. attorney's office have been provided with information about key exchanges of concern to Bezos, the founder of Amazon.com Inc.
Carrie Goldberg, a Brooklyn lawyer representing revenge-porn and sex-crime victims, said Bezos' account laid out a clear case of criminal coercion. When Bezos began to investigate how the National Enquirer came to obtain those messages, he said American Media threatened to release intimate photos of him and Sanchez unless he put a stop to the probe.
It is a federal crime to threaten to injure someone's reputation in exchange for money or a "thing of value", though federal courts haven't made it clear whether a public statement, like the one demanded by AMI, could be considered something of value.
Prosecutors said they would not charge AMI.
Former New York federal prosecutor Jennifer Rodgers said prosecutors are probably weighing the pros and cons of keeping the cooperation agreement in place.
Thus far, Trump has not tweeted about Bezos' blog post. His post, entitled "No thank you, Mr. Pecker", included copies of emails from AMI.
The story recounted by Bezos - the world´s richest man - touches on political intrigue, sexual indiscretion, the murder of a Saudi journalist and bitter charges of media bias.
The revelations appear to show the gossip tabloid trying to smear Bezos - whom Trump has repeatedly attacked as the owner of The Washington Post, a paper he claims is biased against him.
The National Enquirer, whose top boss David Pecker is close to Trump, last month reported Bezos had an extramarital affair with former news anchor and entertainment reporter Lauren Sanchez.
Jeff Bezos's private investigator's suggestion that a "government entity" could have acquired racy pictures of him, coupled with the Amazon CEO's mentions of Saudi Arabia in his blog post targeting the National Enquirer, has fueled speculation about whether the Middle Eastern kingdom is involved in the scandal.
Shortly after that, Bezos opened an investigation into the leak led by Gavin de Becker, a longtime security consultant and former appointee of US President Ronald Reagan.
A person familiar with the National Enquirer's operation, who spoke on the condition of anonymity, told CNN Business that there were indeed similar situations between the National Enquirer and other individuals.
And American Media did not respond to a request for comment about whether law enforcement has been in touch.