The owner of a US gossip magazine accused of blackmail by Amazon founder Jeff Bezos says that it acted in good faith but will conduct an inquiry.

American Media Inc (AMI), the National Enquirer’s parent company, also says it believes it acted lawfully in its reporting on the world’s richest man.

Mr Bezos accused AMI of trying to blackmail him over intimate photos.

He said the company had wanted him to stop investigating how they had obtained his private messages.

Hours after Mr Bezos announced his divorce last month, the magazine had published details, including private messages, of an extramarital affair.

What did Bezos say?

In a stunning blog post on Thursday, he posted an email he said had been sent to his intermediaries by AMI lawyer Jon Fine threatening to publish photos of him and his lover, former TV host Lauren Sanchez.

“Rather than capitulate to extortion and blackmail,” wrote Mr Bezos, “I’ve decided to publish exactly what they sent me, despite the personal cost and embarrassment they threaten.”

The billionaire, who also owns the liberal Washington Post newspaper, said AMI had wanted him to make a “false public statement” that the National Enquirer’s coverage of him and his mistress was not politically motivated.

Mr Bezos included an email in which, according to Mr Bezos, Mr Fine proposed on Wednesday that the photos would not be published in return for a public statement “affirming that [Mr Bezos and his team] have no knowledge or basis” to suspect such a motive.

Mr Bezos’ own investigator had, he claimed, suggested earlier that there were indeed “strong leads” to suspect political reasons.

In his blog post, Mr Bezos mentioned AMI’s links to President Donald Trump.

How did AMI respond?

It said the company believed “fervently that it acted lawfully in the reporting of the story of Mr Bezos”.

AMI said that it had been “in good faith negotiations to resolve all matters with him” when the allegations were made, and that its board had “convened and determined that it should promptly and thoroughly investigate the claims”.

Why did Bezos mention Trump?

He said his ownership of the Washington Post was a “complexifier” for him because he had made enemies of “certain powerful people”, including President Trump, who is a friend of AMI’s boss, David Pecker.

AMI recently admitted in court that it had co-ordinated with the Trump presidential campaign to pay a Playboy model $150,000 (£115,000) in hush money to keep quiet about her alleged affair with Mr Trump.

Mr Bezos noted in his blog post how the publisher had confessed to a “catch and kill” deal to bury Karen McDougal’s politically embarrassing story.

AMI’s agreement to co-operate with federal authorities means it will not face criminal charges over the payments, Manhattan prosecutors announced in December.

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.

A judge confirmed in a court filing on Thursday that federal prosecutors in New York were still investigating campaign finance crimes committed when Cohen paid two women to stay silent about alleged affairs with Trump before he became president.

What about Bezos’ reputation?

“Of course I don’t want personal photos published,” Mr Bezos wrote in his blog post before adding: “I prefer to stand up, roll this log over, and see what crawls out.”

His blog contained itemised details of 10 pictures in an email from National Enquirer editor Dylan Howard, who said they had been “obtained during our newsgathering”.

Dylan Howard’s name, along with those of two National Enquirer reporters, appeared on an 11-page story the magazine published on 9 January containing alleged details of Mr Bezos’ affair with Ms Sanchez.

The tabloid labelled it “the biggest investigation in Enquirer history”.

How did they get the images and messages?

This has been the focus of Mr Bezos’ private investigators.

The inquiry has been led by Gavin de Becker, who is the billionaire’s long-term head of security.

Last week he said Lauren Sanchez’s brother, Michael, had become one of the focuses of their investigation.

Mr Sanchez, a publicist who lives in West Hollywood, has strongly rejected involvement.

“I am not dignifying de Becker’s passive aggressive allegations or his crazy conspiracy theories,” he said in a statement to Page Six. He also said he had recommended his sister fire Mr de Becker.

US media report that Mr Sanchez knows AMI’s David Pecker – as well as other people with links to Mr Trump including his former campaign aides Carter Page and Roger Stone.

Mr Stone was indicted by the special counsel’s Russia investigation last month.

He has confirmed to the Daily Beast that he knows Mr Sanchez – describing him as a “very good guy”.