Fox News anchor Bret Baier wanted the network to withdraw its famous call of Arizona for Joe Biden on election night in 2020, citing pressure from Donald Trump’s campaign and saying the swing state should be “put back in his column”, a new book says.

News of Baier’s email is contained in The Divider: Trump in the White House 2017-2021, published in the US on Tuesday.

The authors, Peter Baker of the New York Times and Susan Glasser of the New Yorker, call Baier’s request “stunning”, as Arizona “was never in Trump’s column. While the margin of his defeat in the state had narrowed since election night, he still trailed by more than 10,000 votes.”

Trump did win Arizona in 2016. Its call for Biden four years later did not give the Democrat the White House but it did signal Trump was in deep trouble. Accounts of his fury at the surprisingly early call, which other networks did not follow, are legion.

According to the author Michael Wolff, Rupert Murdoch, the owner of Fox News, both personally approved the call and said of Trump: “Fuck him.”

Fox News denied that but Jared Kushner, Trump’s son-in-law, wrote in his own book that on election night, Murdoch told him Arizona was “not even close”.

The election was called for Biden on 7 November, four days later, when he was agreed to have won Pennsylvania.

But Baker and Glasser report that “turmoil” reigned at Fox News over Arizona, amid worries that rightwing rivals including Newsmax, firmly in the van for Trump, might take viewers away.

“Fox executives were freaking out,” the authors write, adding that Suzanne Scott, the chief executive, wanted Fox News to stop calling any more states until they were certified by election authorities – a process that takes weeks.

Baker and Glasser say Bill Sammon, the Washington managing editor, rejected that plan, saying: “Our enemies – and there are many – will portray this as follows: For the first time in its history, Fox News refuses to project the next president, who just happens to be the Democrat who defeated Donald Trump.”

Baker and Glasser report that though Baier had “long insisted that he was different than the Trump-cheerleading opinion hosts” at Fox News, he felt White House pressure to rescind the Arizona call.

In an email on Thursday 5 November, they report, the anchor said “the Trump campaign was really pissed” and added: “This situation is getting uncomfortable. Really uncomfortable. I keep having to defend this on air.”

Baier reportedly “accused the [Fox News] Decision Desk of ‘holding on for pride’ and added: ‘It’s hurting us. The sooner we pull it – even if it gives us a major egg – and we put it back in his column, the better we are in my opinion.’”

They also say the Decision Desk was not allowed to call Nevada for Biden even after other networks did, because doing so would have made Biden Fox News’s projected winner, given the Arizona call.

Trump continues to lie about mass voter fraud in Arizona, even after an “audit” by state Republicans did not find fraud – and instead slightly increased Biden’s margin of victory.

In the aftermath of the Arizona call, Baker and Glasser write, Bill Sammon and Chris Stirewalt, senior members of the Fox News politics team, were “summarily fired”.

Fox News insists Sammon retired while Stirewalt – who has written his own book – was let go because of “restructuring”.

Baker and Glasser write: “Whatever they called it, Fox had decided that deference to Trump was more important than getting the story right.”

Quoting another email, they say Jay Wallace, the Fox News president and executive editor, told Sammon: “I respect the hell out of you, but it’s turned into a war.”