"The Kennedy family did have some part ... in the release," King says in the recording, which was discovered in 2012. "But I must make it clear that many other forces worked to bring it about also."
A copy of the original recording will be played for visitors at the National Civil Rights Museum in Memphis for a "King Day" event on Jan. 20.
King was arrested a few weeks before the presidential election at an Atlanta sit-in. Charges were dropped, but King was held for allegedly violating probation for an earlier traffic offense and transferred to the Georgia State Prison in Reidsville, Ga.
The Kennedys intervened, and King was released. Their intervention won the support of black voters who helped give Kennedy the winning edge in several key states.
Despite their help, however, King was careful not to give them too much credit.
"I think Dr. King was aware in the tape that he probably did more for John F. Kennedy than perhaps John F. Kennedy did for him," said Keya Morgan, a New York-based collector and expert on historical artifacts. Morgan acquired the reel-to-reel audiotape from Chattanooga, Tenn., resident Stephon Tull, who discovered it while cleaning out his father's attic.
Raymond Winbush, director of the Institute for Urban Research at Maryland's Morgan State University, said Kennedy's call to King's wife was political in nature because the Kennedys had been slow to get involved in the civil rights movement.
He said John Kennedy didn't actually commit to the movement until a few months before his assassination when civil rights leader Medgar Evers was gunned down by a Klansman outside his Jackson, Miss., home just after midnight on June 12, 1963.
The slaying came hours after JFK's television speech in support of civil rights and helped propel the struggle for equality to national attention.
"There were a lot of black folks who ... weren't fully committed to his campaign," said Winbush, who is also a historian and psychologist. "That call he made to Coretta moved black folks."
He said King's comments on the tape were measured because he probably didn't want to offend black supporters, like the NAACP, that had also aided him.
"He kind of went in the middle," Winbush said.
Tull, the Chattanooga man who discovered the tape, said his father had planned to write a book about the racism he encountered growing up in Chattanooga and later as an adult. Tull said his dad, an insurance salesman, interviewed King when he visited the city, but never completed the book and just stored the recording with some other interviews he had done. Tull's father is now in his late 80s and under hospice care. Tull has asked that his father not be identified.
In the recording, King also discusses his definition of nonviolence, his visit to Africa and the impact of the civil rights movement.
"I am convinced that when the history books are written in future years, historians will have to record this movement as one of the greatest epochs of our heritage," he said.