"You reduced him to the nut house," Kennedy said after Nixon's infamous "last news conference," which followed his loss to Brown. "That last farewell speech of his ... shows that he belongs on the couch."
After the defeat, Nixon bitterly told reporters: "You won't have Nixon to kick around anymore."
The conversation was included on tapes released last month by the John F. Kennedy Library in Boston, the San Francisco Examiner reported Sunday.
On the tapes, Brown also told the president that humiliating Nixon was what Kennedy had wanted. Kennedy defeated Nixon for the presidency in 1960.
"This is a very peculiar man," Brown said. "I really think that he is psycho. He's an able man, but he's nuts!"
Brown told Kennedy that Nixon may have doomed his political future in California with the farewell speech. Six years later, Nixon carried the state in his successful presidential bid against Hubert H. Humphrey.