Federal prosecutors are investigating whether the the National Enquirer's parent company violated a cooperation deal with the US Southern District of New York after Amazon CEO Jeff Bezos published a blog alleging the tabloid attempted to blackmail him over an affair.

Mr Bezos — the world's richest man, and a frequent target of Donald Trump's ire — wrote in a blog post on Thursday that the parent company of the tabloid had attempted to force him to release what he said would be a false statement that the organisation's reporting on his private life was not politically motivated. Mr Bezos's post came a month after the National Enquirer published lurid texts between the billionaire and former Fox TV anchor Lauren Sanchez, prompting the Amazon founder to announce he is getting a divorce.

In his post on Medium, Mr Bezos charged that representatives for the Enquirer's parent company— American Media Inc, which is owned by a close ally of Mr Trump's, David Pecker — had threatened to releease further photos Mr Bezos had sent to Ms Sanchez. In emails posted in the blog, representatives of the company can be seen allegedly making the threats.

::Read more about Mr Bezos's Medium post, and the full allegations made, here::

Mr Bezos wrote in his post that the emails were prompted by a the company's interest in silencing him after he launched a private investigation into the means by which the National Enquirer had obtained the texts.

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“A few days after hearing about Mr Pecker’s apoplexy, we were approached, verbally at first, with an offer. They said they had more of my text messages and photos that they would publish if we didn’t stop our investigation,” Mr Bezos wrote.

The new investigation into the National Enquirer's parent company appears to follow after the company agreed to cooperate with investigators after it was determined it had worked to faciliatata hush payment between Mr Trump and former Playboy playmate Karen acDougal, who alleges she had an affair with him before he became president. Mr Trump has denied the affair, as well as other affairs that have been alleged since his election.

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In agreeing to cooperate, AMI admitted to facilitating that payment in the run up to the 2016 election.

"AMI admitted that it made the $150,000 payment in concert with a candidate's presidential campaign, and in order to ensure that the woman did not publicize damaging allegations about the candidate before the 2016 presidential election," the Southern District of New York (SDNY) said in a statement announcing the agreement.