The Georgia Republican responsible for running elections considered an infamous call in which Donald Trump told him to “find” enough votes to overturn Joe Biden’s victory in the state a “threat” to his safety and that of his family.

Biden’s victory in Georgia was a narrow but vital part of his national win. No Democratic presidential candidate had taken the state since Bill Clinton in 1992.

Trump called Brad Raffensperger, the Georgia secretary of state, nearly two months after election day, on Saturday 2 January. Telling him “it’s pretty clear we won”, the then president said: “I just want to find 11,780 votes, which is one more than we have [to get]” to surpass Biden’s total.

Raffensperger, a conservative who supported Trump, resisted the president’s demands. That prompted Trump to suggest the refusal to expose mass voter fraud in Georgia – on which Trump insisted but which did not exist, as in all other states – could be a “criminal offense”.

“That’s a big risk to you,” Trump said. “That’s a big risk.”

In Integrity Counts, a book published on Tuesday, Raffensperger writes: “I felt then – and still believe today – that this was a threat. Others obviously thought so, too, because some of Trump’s more radical followers have responded as if it was their duty to carry out this threat.”

Raffensperger details death threats texted to his wife, an encounter with men who may have been staking out his home, and being escorted out of the Georgia state capitol on 6 January as rightwing protesters entered.

A recording of Trump’s call was released to the Washington Post and became a key exhibit in Trump’s second impeachment trial, for inciting the deadly attack on the US Capitol on 6 January, by supporters seeking to overturn the election.

Trump was acquitted when only seven Republican senators could be persuaded to vote for his guilt. He remains free to run for president again and dominates the Republican party but his attempts to overturn his defeat in Georgia have contributed to his extensive legal jeopardy.

The Fulton county district attorney, Fani Willis, is investigating. Raffensperger told the Associated Press investigators “talked to some of our folks here. We sent all the documents and she can now buy the book online”.

The Associated Press contributed to this report