Shortly before the January 6 insurrection, Donald Trump warned Mike Pence he was “too honest” when he hesitated to pursue legalistic attempts to stop certification of Joe Biden’s 2020 election victory and would make Trump’s supporters “hate his guts”, the former vice-president writes in his memoir.

Pence also seems, bizarrely, to blame the anti-Trump Lincoln Project for enraging Trump with a political ad, thereby fueling the anger that incited the Capitol attack.

Pence’s book, So Help Me God, will be published in the US on Tuesday. An extract was published by the Wall Street Journal on Wednesday.

Describing a conversation on New Year’s Day 2021, five days before supporters Trump told to “fight like hell” stormed the US Capitol, Pence writes that he and Trump discussed a lawsuit filed by Republicans, asking a judge to declare the vice-president had “‘exclusive authority and sole discretion to decide which electoral votes should count”.

Pence says Trump told him that if the suit “gives you the power, why would you oppose it?”

Pence says he “told him, as I had many times, that I didn’t believe I possessed that power under the constitution”.

“You’re too honest,” Trump chided. “Hundreds of thousands are gonna hate your guts … People are gonna think you’re stupid.”

In the end, hundreds of Trump supporters stormed the Capitol, some chanting that Pence should be hanged. Nine deaths, including law enforcement suicides, have been linked to the riot.

Pence’s book emerges as he seeks to establish himself as an alternative to Trump in the Republican presidential primary for 2024.

Trump has indicated he will announce his third consecutive run soon, a plan possibly delayed by midterm elections on Tuesday in which the GOP did not succeed as expected and high-profile Trump-backed candidates failed to win their races.

Ron DeSantis, the Florida governor and a much stronger rival to Trump in polling than Pence, provided a bright spot for Republicans with a landslide win that thrust his name back into the spotlight.

In hearings held by the House January 6 committee, Pence has been painted as a hero for refusing to attempt to block Biden’s win, even after his life was placed in danger.

In the extract published on Thursday, Pence said the Lincoln Project, a group of anti-Trump conservative operatives, angered Trump with an ad which said Pence would “put the final nail in the coffin” of his re-election campaign by certifying Biden’s win.

Rick Wilson, a Lincoln Project co-founder, told the Guardian: “It’s no secret that the Lincoln Project has lived rent-free in Donald Trump’s head since 2019. Mike Pence telling this story is one more powerful testimony to just how our ‘audience of one’ strategy unfailingly disrupts Trump world.”

On Twitter, Wilson linked to the ad.

On the page, Pence describes events inside the Capitol as Trump’s supporters attacked. His account parallels reporting by news outlets and testimony presented by the House committee, to which Pence has not yet testified.

The devoutly Christian Pence gives his version of a call with Trump on the morning of 6 January in which Trump has widely been described as calling his vice-president a “pussy”.

Pence writes: “The president laid into me. ‘You’ll go down as a wimp,’ he said. ‘If you [don’t block certification], I made a big mistake five years ago!’”

Pence describes his refusal, also widely reported, to get in a Secret Service vehicle, lest his protectors drive him away while the attack was in motion.

He describes meetings with Trump after the riot, when Trump’s second impeachment was in train. On 11 January, Pence writes, Trump “looked tired, and his voice seemed fainter than usual”. He says Trump “responded with a hint of regret” when he was told Pence’s wife and daughter were also at the Capitol during the deadly attack.

“He then asked, ‘Were you scared?’

“‘No,’ I replied, ‘I was angry. You and I had our differences that day, Mr President, and seeing those people tearing up the Capitol infuriated me.’ He started to bring up the election, saying that people were angry, but his voice trailed off. I told him he had to set that aside, and he responded quietly, ‘Yeah.’”

Pence claims the Capitol rioters, more than 900 of whom have now been charged, some with seditious conspiracy, were “not our movement”. He says Trump spoke with “genuine sadness in his voice” as he “mused: ‘What if we hadn’t had the rally? What if they hadn’t gone to the Capitol? … It’s too terrible to end like this.’”

Pence may risk angering Trump by presenting something approaching presidential contrition. Trump claims to regret nothing about his actions on 6 January, denying wrongdoing in the face of multiple investigations, pursuing the lie that his defeat was the result of electoral fraud and presenting rioters as political prisoners.

Pence also describes a meeting on 14 January, “the day after President Trump was impeached for the second time”.

“I reminded him that I was praying for him,” Pence writes. Trump, he says, answered “Don’t bother” but added: “It’s been fun.”

Pence said he told Trump they would “just have to disagree on two things” – January 6 and the fact Pence would “never stop praying” for Trump.

Pence says Trump smiled and said: “That’s right – don’t ever change.”