On election night last year Rupert Murdoch reportedly gave his son Lachlan permission for Fox News to call Arizona for Joe Biden, a decision that signalled Donald Trump’s defeat, with “a signature grunt” and a pithy barb: “Fuck him.”

The news is sure to anger Trump as he pushes his lie that he lost the White House because of electoral fraud. It is contained in Michael Wolff’s third book on the Trump presidency, Landslide, which will be published next week.

The Daily Beast first reported Murdoch’s remark.

Wolff, a former Guardian columnist, is one of a number of authors who have interviewed Trump for new books. Wolff has also written widely about the Murdochs and Fox News. In Landslide, he writes that “the marriage between Trump and the Murdochs, in some ways the foundation of the Trump movement, was quite a sadomasochistic one”.

The Arizona call was particularly punishing for Trump. Shortly after 11pm ET on 3 November, Wolff writes, Lachlan Murdoch was told by the Fox News decision desk it was ready to call the state for Biden.

It was, Wolff writes, “still, by most measures, hotly contested and still a definite Trump win” in one forecasting model. But the decision desk was “independent of Fox News’ otherwise partisan views [if] merely as [a way] to bypass the news desk and to be directly answerable to the Murdochs”.

Delaying the Arizona call would have been defensible, Wolff writes, given the closeness of the contest. But Lachlan Murdoch called his father and asked if he wanted to make a call which was sure to anger Trump. Reportedly, Rupert did.

In a statement emailed to the Guardian on Friday, a Fox News spokesperson called Wolff’s account “completely false”.

“Arnon Mishkin who leads the Fox News decision desk made the Arizona call on election night and Fox News Media president Jay Wallace was then called in the control room. Any other version of the story is wildly inaccurate.”

Wolff also reports the scene at the White House, where he says Trump was being assured by “merry” and “untroubled” aides “about how good everything looked” before one aide, Jason Miller, was told Fox News was going to call Arizona for Biden.

“Miller involuntarily rose from his seat,” Wolff writes. “‘What the fuck?’ he said out loud.”

Electoral college results from Arizona and Pennsylvania were the subject of formal objections from Republicans in Congress on 6 January, the day a mob incited by Trump attacked the Capitol, resulting in five deaths.

Trump was impeached and acquitted. Fox News has remained behind him as he pushes his electoral fraud lie while controlling a party seeking to block investigation of 6 January, to restrict voting access and to make it easier to overturn election results.

In Arizona’s most populous county, a controversial and partisan ballot audit goes on.

The decision to call the state cost some at Fox News dear. One editor, Chris Stirewalt, has said he was subjected to “murderous rage” from Trump supporters.

Murdoch’s dismissal of Trump, while blunt, should not entirely be a surprise. In his first of three books on the Trump presidency, Fire and Fury, Wolff recounted the fallout from a meeting in 2016 between the president-elect and big tech executives.

Wolff reported that Trump called Murdoch to enthuse about how he was going to help big tech more than Barack Obama.

Murdoch, Wolff writes, got off the phone, shrugged and said: “What a fucking idiot.”