Stuart Collier, the reporter at the centre of the incident almost three decades ago, said he believed that Mr Johnson was unfit to be prime minister.
In 1990, Mr Johnson was secretly recorded agreeing to provide Mr Collier's address to friend Darius Guppy, who wanted to arrange for the journalist to have his ribs cracked in revenge for investigating his activities.
In the event no attack took place, and after the recording came to light in 1995, Mr Johnson - who had been the Brussels correspondent of The Daily Telegraph at the time - dismissed the conversation as a joke.
However, Mr Collier, 69, who had been working for the News of the World, told The Guardian that although he had only found out about it long after the fact, it had left him worried for the safety of his family.
He said he thought it was "disgraceful" that Mr Johnson could be prime minister and said he should "definitely apologise".
"I didn't treat it as a joke. That's why I warned my wife to be careful about who she answered the door to," he said.
"I took it seriously at the time and it concerned me. I was worried, certainly worried enough to put my wife on a warning."
Mr Collier's wife, Jennifer, added: "He should be accountable for the things that he's done. I think it's disgraceful behaviour."
In the call, Mr Guppy was recorded saying: "I am telling you something, Boris, this guy has got my blood up, all right, and there is nothing which I won't do to get my revenge. It's as simple as that."
When he was questioned about it in a BBC interview in 2013, Mr Johnson said: "It was certainly true that he was in a bit of a state, and I did humour him in a long phone conversation, from which absolutely nothing eventuated."
There was no immediate response from Mr Johnson's campaign team for a request for a comment.