The Guardian newspaper said the document, obtained by investigative journalist Eric Schlosser under the Freedom of Information Act, gave the first conclusive evidence that the United States came close to a disaster in January 1961.
The incident happened when two Mark 39 hydrogen bombs were accidentally dropped over Goldsboro, North Carolina, after a B-52 bomber broke up in midair.
There has been persistent speculation about how serious the incident was and the U.S. government has repeatedly denied its nuclear arsenal put Americans' lives at risk through safety flaws, the newspaper said.
But the newly published document said one of the two bombs behaved exactly in the manner of a nuclear weapon in wartime, with its parachute opening and its trigger mechanisms engaged. Only one low-voltage switch prevented a cataclysm.
Fallout could have spread over Washington, Baltimore, Philadelphia and even New York City, the paper said, threatening the lives of millions of people.
In the document, Parker Jones, a senior engineer in the Sandia National Laboratories responsible for the mechanical safety of nuclear weapons, concluded that "one simple, dynamo-technology, low-voltage switch stood between the United States and a major catastrophe."
Jones' report, titled "Goldsboro Revisited or: How I Learned to Mistrust the H-Bomb," was written eight years after the accident in which one hydrogen bomb fell into a field near Faro, North Carolina, and the other into a meadow.
He found that three of four safety mechanisms designed to prevent unintended detonation failed to operate properly in the Faro bomb.
When the bomb hit the ground, a firing signal was sent to the nuclear core of the device and it was only the final, highly vulnerable switch that averted a disaster.
"The MK 39 Mod 2 bomb did not possess adequate safety for the airborne alert role in the B-52," Jones concluded.
The Guardian said the document was found by Schlosser as he was researching a new book on the nuclear arms race, "Command and Control."