The story comes from The Telegraph.
Secret Service agent 'almost shot Mahmoud Ahmadinejad'
The event happened in 2006 outside the InterContinental Hotel in New York during a United Nations assembly.
The agent had reportedly been adjusting a shotgun on the side of an armoured car, that was waiting for President Bush when the weapon was accidentally fired in the direction of the Mr Ahmadinejad.
A memo, quoted in the book 'Deep State: Inside the Government Secrecy Industry', was reportedly sent whilst the Bush administration tried to work out how to deal with the situation.
The memo, sent as part of Mr Bush's daily intelligence briefing read: "A US Secret Service agent, in an apparent accident, discharged his shotgun as Iranian President Mahmoud Ahmadinejad was loading his motorcade at the InterContinental Hotel yesterday".
An official quoted in the book said: "When I read that, I remember closing my eyes".
"Everyone just stopped" an official also quoted in the book recalled, "The Iranians looked at us. We looked at the Iranians. The agent began to apologise. Ahmadinejad just turned his head and got into the car".
At the time Iran was under scrutiny as a report, published only a few days before the event, by the International Atomic Energy Agency, had concluded that the country had not suspended "uranium-enrichment-related activities".
The US was in talks with the rest of the Security Council as to how best to deal with the situation.
There were fears that, the Iranians would claim this was an attempted assassination on their President by the US, thus resulting in a potential public relations disaster.