"Her life is dedicated to putting me down but I attempt very strongly not to put her down," McCartney, 63, reportedly said of John Lennon's widow.
"She's John's wife so I have to respect her for that, but I don't think she's the brightest of buttons. She's said some particularly daft things in her time," McCartney was quoted as saying in Monday's Daily Mirror.
Ono, 72, said last week in London that Lennon used to be obsessed with why McCartney's songs were more popular than his own.
"I said, 'You're a good songwriter," she said. "It's not June with spoon you write.'"