According to Amazon boss Jeff Bezos, David Peker would use blackmail to stop his investigation of how the National Anchor had received his personal pictures and messages.
The journal has previously published photos that show Bezos with his mistress Lauren Sanchez.
Bezos is now in divorce with Mrs. Mackenzie. They have been married for 25 years, CNN writes.
Threatened with more pictures
Jeff Bezos himself wrote a posting on the Medium site for his feelings after the publication.
"Of course, I do not want to publish my personal pictures, but I do not want to participate in their well-known methods of extortion, political services, political attacks and corruption," Jeff Bezos writes.
In the publication Jeff Bezos published what he claims to be an email from American Media Inc., the company that owns the National Enquirer and is run by David Pecker.
In the e-mail, the company's representative, according to Bezos, wrote that they had more personal photos, including naked pictures, and that they intended to publish them if Bezos did not agree with specific requirements.
Bezos has stopped writing critically about the newspaper and has to declare that the photos are not published for political reasons.
Pecker paid a model for his silence
David Peker has a long-standing relationship with President Donald Trump.
In December, the US media said they were paying a woman to muffle her story about a supposed deal with Donald Trump.
According to the AP, the woman, Playboy's model Karen McDougall, received almost 1.4 million for her silence.
"They wanted to lower it to make Trump happy"
The Washington Post reported that Bezzo's private security consultant suspected that Loren Sanchez's brother, Michael Sanchez, was involved in the leak of personal photos. The Washington Post is owned by Jeff Bezos.
Michael Sanchez told the Washington Post that the National Enquirer wanted to hurt Bezos to delight Trump.
"They will lower it to make Trump happy," Michael Sanchez told the Washington Post.
American Media Inc., in a statement to the Washington Post, denied being affected by outsiders in its decision to publish the images.