The retired NBA star and TNT commenter angered some San Antonio residents when he mocked the city's "big ol' women" last week during a broadcast of Inside the NBA.
"That's a gold mine for Weight Watchers," he said. "Victoria is a secret down there."
Though his comments launched a firestorm of criticism in San Antonio, Barkley has said he won't apologize.
"Turn off your d*** televisions," Barkley said during TNT's playoff coverage on Sunday.
"If you don't like me or the show, turn it off. And they want me to apologize. That's not going to happen. That's not gonna happen," he added. "You all can write letters to your momma, your daddy, your uncle. I'm going to have fun on television. You know that I'm joking around. But if y'all waiting on me to apologize, hell gonna freeze over."
Three city councilwomen responded to Barkley in a YouTube video, in which they lauded San Antonio's physical fitness awareness programs and mocked Barkley's "tight shorts in the 80's."