American Media and the National Enquirer tabloid newspaper shredded sensitive documents about Donald Trump shortly before the 2016 election, the reporter Ronan Farrow alleges in a book published on Tuesday.

In Catch and Kill: Lies, Spies, and a Conspiracy to Protect Predators, Farrow writes that the shredding happened in the first week of November 2016, on the day the Wall Street Journal reported a Playboy model’s claim to have had an affair with Trump and American Media’s role in keeping the story quiet. That process is referred to in the title of Farrow’s book.

According to Farrow, Dylan Howard, then editor of the Enquirer, ordered a staffer to “get everything out of the safe” and said “we need to get a shredder down there”.

Farrow writes: “The staffer opened the safe, removed a set of documents, and tried to wrest it shut. Later, reporters would discuss the safe like it was the warehouse where they stored the Ark of the Covenant in Indiana Jones, but it was small and cheap and old.”

Farrow quotes an employee of the Enquirer as saying “a larger than customary volume of refuse” was collected from the Enquirer offices later the same day.

He also quotes a “senior AMI employee” as saying: “We are always at the edge of what’s legally permissible. It’s very exciting.”

On CNN on Monday morning, Farrow said the safe contained details of alleged consensual affairs and payoffs and also allegations of assault by Jill Harth, who in a 1997 complaint accused Trump of “attempted ‘rape’”. In October 2016, amid a flood of allegations of sexual misconduct by Trump, she stood by that allegation in an interview with the Guardian.

The Enquirer endorsed Trump and published negative stories about his opponent, Hillary Clinton.

Farrow’s claims were reported before the book’s publication by outlets including Politico, CNN and the Daily Beast.

An attorney for Howard said in a statement the former editor would not comment, “while all legal options and jurisdictions are being considered”.

A spokesman for American Media said in a statement: “Mr Farrow’s narrative is driven by unsubstantiated allegations from questionable sources and while these stories may be dramatic, they are completely untrue.”

Catch and Kill has also sparked intense controversy over its coverage of sexual assault allegations against the movie mogul Harvey Weinstein and NBC host Matt Lauer, which both men deny.

The book is the subject of legal threats around the world but still went on sale on Tuesday.

In an interview with the Guardian published last weekend, Farrow said the factchecking process had been so rigorous, one factchecker “got a stress nosebleed”.

“I’ll let the reporting in the book stand on its own,” Farrow told CNN.

Farrow writes that the safe which held the Trump material belonged to Barry Levine, then executive editor of the Enquirer. Levine is now co-author, with Monique El-Faizy, of the forthcoming book All the President’s Women: Donald Trump and the Making of a Predator.

An excerpt of that book published in Esquire last week said 43 women were making new allegations of inappropriate sexual behaviour by Trump.