American Media insisted on Friday that it "acted lawfully" in reporting about Amazon CEO Jeff Bezos' extramarital affair, but said it will "promptly and thoroughly investigate the claims."

In a bombshell blog post Thursday, Bezos accused the National Enquirer's publisher of threatening to post sexual pictures that the billionaire had texted to his mistress, accusing AMI of blackmail and extortion.

AMI's denial follows an immunity deal struck in December with federal prosecutors investigating President Donald Trump's former lawyer and fixer, Michael Cohen, requiring the supermarket tabloid publisher to commit no crimes. AMI's board of directors has four people, including its chairman, David Pecker, a longtime friend of Trump.

Later Friday, news outlets reported that federal prosecutors for the Southern District of New York are reviewing the Enquirer's handling of Bezos' affair to determine whether the tabloid had breached its immunity agreement.

AMI claimed that when Bezos accused it of blackmail, it was already "in good faith negotiations to resolve all matters with him."

The statement, provided by a company spokesman to CNBC, continued: "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."

Bezos wrote that "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."

AMI's assertion that it violated no laws in its reporting matters beyond the Bezos affair. In December, the tabloid publisher struck an immunity deal with federal prosecutors in connection with the $150,000 hush-money payment the supermarket tabloid gave to a Playboy model who claims she had an affair with Trump.

That agreement requires that AMI "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.

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.