Giuliani said he felt like he was "shot" after a grocery store employee slapped his back.
Giuliani said he could have "hit the ground" and cracked his skull if he hadn't been more fit.
However, footage of the incident showed a man slapping Giuliani on the back before walking on.
Footage has emerged of what former New York mayor Rudy Giuliani called an attack that could have resulted in him falling, cracking his skull, and dying.
Giuliani was at a ShopRite grocery store on Staten Island when he claimed to have been assaulted by a man. Giuliani had been out campaigning for his son Andrew, who is running as a GOP candidate in the race for the New York governorship.
Giuliani later called a radio show hosted by former New York mayoral candidate Curtis Sliwa to talk about the incident. The former mayor said that he had just exited the store's men's room and was caught up with a group of people who were "hugging" and "kissing" him when the assault occurred.
"I feel a shot on my back like somebody shot me. I went forward, but luckily I didn't fall down," Giuliani said.
"The guy says words I can't repeat. You effin' whatever. And then he goes on and on and on yelling and screaming, he moves away, yelling and screaming. Things like 'You're gonna kill women,'" Giuliani said, adding that the man was a ShopRite employee who looked "either drunk or high."
"I mean, suppose I was a weaker 78-year-old and I hit the ground, cracked my skull, and died," the former mayor said.
Giuliani made similar claims to The New York Times about the incident.
"My back hurts, but otherwise I'm able to walk and stuff like that," he told The Times, adding that he had "red marks" on his back after the incident.
"We will not be intimidated by left-wing attacks," Giuliani's son, Andrew Giuliani, told NBC following the incident. "As governor, I will stand up for law and order so that New Yorkers feel safe again."
Footage of the attack released by The New York Post did not appear to show Giuliani lurching forward or falling after being slapped on the back. The video also appeared to show Giuliani standing upright and pointing his finger at the man who confronted him.
The Times reported that the man involved in the incident with Giuliani was a grocery store worker at the Charleston ShopRite that Giuliani was visiting.
The New York Police Department told The Times that the 39-year-old employee had slapped Giuliani on his back while saying, "What's up, scumbag," and added that investigations into the matter were ongoing.
Axios reported that the unnamed man will face a second-degree assault charge for the incident.