Goaded by "Fox & Friends" hosts on Friday morning, Petty accepted Stewart's offer to set up a head-to-head race between Patrick and the NASCAR Hall of Famer.
"I'm 76 years old, OK?" Petty said, grinning, during a live spot from Daytona International Speedway. "It's been 25 years since I've been in a race car. But I'll take that challenge."
When pressed, he reaffirmed, "Oh, yeah. When is this going to happen?"
Stewart had previously told Performance Racing Network that Patrick should challenge NASCAR's all-time leader in wins (200) and co-holder of the championships record (seven) to a match race in equally prepared cars.
"I think that (a race) would pretty much settle it once and for all, maybe get him to shut up a little bit, too," Stewart said. "I will supply the cars. If he wants to race her, I'll make sure they have exactly the same setup in the car and give him the chance. He can drive one of my 14 cars. I don't care."
And if Patrick were to win the race, Stewart said, "If I were her, I'd take (the checkered flag) over there and cram it up his (butt)."
Petty made his original comments about Patrick during a recent appearance at the Canadian Motorsports Expo, stating that, "If she'd have been a male, nobody would ever know if she'd showed up at a racetrack."
Patrick finished 27th in the Sprint Cup standings during her rookie season, driving the No. 10 Chevrolet for Stewart-Haas Racing. Her highlight came in the season-opening Daytona 500, where she finished eighth after becoming the first woman to win the pole for that event.
That is her only top-10 finish in 46 races at NASCAR's highest level. Before that, she amassed seven top-10 finishes and one pole in 60 races over four seasons in the Nationwide Series.
Petty has stood by his remarks but asserted that he is not a sexist.
When asked by Fox hosts about his critique of Patrick's career, he stated, "I judge by results."