In a forthcoming memoir, Jared Kushner says he personally intervened to stop Donald Trump attacking Rupert Murdoch in response to the media mogul’s criticism, at the outset of Trump’s move into politics in 2015.

In the book, Breaking History, Kushner writes: “Trump called me. He’d clearly had enough. ‘This guy’s no good. And I’m going to tweet it.’

“‘Please, you’re in a Republican primary,’ I said, hoping he wasn’t about to post a negative tweet aimed at the most powerful man in conservative media. ‘You don’t need to get on the wrong side of Rupert. Give me a couple of hours to fix it.’”

Kushner says he fixed it. If his claim is true, he could be seen to have made a hugely consequential intervention in modern US history.

Murdoch’s support, chiefly through Fox News, did much to boost Trump to victory over Hillary Clinton in 2016. Despite persistent reports of friction between the two men, Murdoch supported Trump through four tumultuous years in power which culminated in Trump’s refusal to admit defeat and the deadly attack on Congress.

The Guardian obtained a copy of Kushner’s book, which will be published next month.

The book lands at a time when Murdoch’s newspapers and to some extent Fox News are widely seen to be pulling away from Trump, amid congressional hearings into his election subversion and the January 6 attack, speculation about criminal charges and as he prepares another White House run.

In his book, Trump’s son-in-law, who became a senior White House adviser, describes a friendship with Murdoch built on time on Murdoch’s yacht and at Bono’s house in France, watching the U2 frontman sing with Bob Geldof and Billy Joel. Kushner also describes how Wendi Murdoch, Rupert Murdoch’s third wife, helped get him back with Ivanka Trump after a breakup.

Kushner claims to have convinced Murdoch to support Trump in 2015.

Trump and Murdoch were not close before Trump entered politics. But in July 2015, after Trump launched his explosive campaign for the Republican presidential nomination with a racist rant about Mexicans, the Fox News owner tweeted: “When is Donald Trump going to stop embarrassing the whole country?”

A week later, the New York Times described Murdoch disparaging Trump. Trump was furious and threatened to tweet. Kushner was not then an official adviser to his father-in-law but he writes: “I called Rupert and told him I had to see him.

“‘Rupert, I think he could win,’ I said, as we sat in his office. ‘You guys agree on a lot of the issues. You want smaller government. You want lower taxes. You want stronger borders.’

“Rupert listened quizzically, like he couldn’t imagine that Trump was actually serious about running. The next day, he called me and said, ‘I’ve looked at this and maybe I was misjudging it. He actually does have a real following. It does seem like he’s very popular, like he can really be a kingmaker in the Republican primary with the way he is playing it. What does Donald want?’

“‘He wants to be president,’ I responded.

“‘No, what does he really want?’ he asked again.

“‘Look, he doesn’t need a nicer plane,’ I said. ‘He’s got a beautiful plane. He doesn’t need a nicer house. He doesn’t need anything. He’s tired of watching politicians screw up the country, and he thinks he could do a better job.’

“‘Interesting,’ Rupert said.

“We had a truce, for the time being.”

Kushner also writes about Trump’s clashes with Fox News during the 2016 campaign, including a clash with the anchor Megyn Kelly. Kushner says he agreed a deal with Roger Ailes, then in charge of Fox News, for a donation of $5m to a veterans’ organisation of Trump’s choice, in return for Trump choosing not to skip a debate.

Murdoch rejected the deal, Kushner writes, saying if he took it he would have to “pay everyone to show up to debates”.

Kushner also describes how Murdoch helped shape his view of why the US needed Trump. At a rally in Springfield, Illinois in November 2015, Kushner was reminded “of a book that Rupert Murdoch had given me months earlier: Charles Murray’s Coming Apart, which makes a case that over the last 50 years America has divided into upper and lower classes that live apart from each other, geographically and culturally”.

Trump, Kushner writes, appealed to the “forgotten and disenfranchised”. For his son-in-law rally in Illinois “was a wake-up call”.

Kushner’s version of another call with Murdoch, on election night 2020, has been widely reported. He says Murdoch told him Fox News’s call of Trump’s defeat by Joe Biden in Arizona, a decision which infuriated the president and his advisers, was “ironclad – not even close”.

Arizona played a central role in Trump’s attempt to overturn the election through lies about voter fraud. Fox News is now the subject of a $1.6bn defamation suit from a maker of voting machines, over conspiracy theories pushed by Trump and his allies and repeated on the network.

Fox News has said it is “confident we will prevail as freedom of the press is foundational to our democracy and must be protected, in addition to the damages claims being outrageous, unsupported and not rooted in sound financial analysis, serving as nothing more than a flagrant attempt to deter our journalists from doing their jobs”.