"I think I could have said it better," he told nationally syndicated radio host Mike Gallagher. "You know, what I was saying was, 'I'm there with you."'
The former New York mayor upset some firefighters and police officers when he said Thursday in Cincinnati that he was at ground zero "as often, if not more, than most of the workers."
"I was there working with them. I was exposed to exactly the same things they were exposed to. So in that sense, I'm one of them," he told reporters at a Los Angeles Dodgers-Cincinnati Reds baseball game.
Fire and police officials responded angrily, saying Giuliani did not do the same work as those involved in the rescue, recovery and cleanup from the 2001 terrorist attacks, which left many workers sick and injured.
On Friday, Giuliani said he was trying to show his concern for the workers' health.
"What I was trying to say yesterday is that I empathize with them, because I feel like I have that same risk," he said.
"There were people there less than me, people on my staff, who already have had serious health consequences, and they weren't there as often as I was," Giuliani said, "but I wasn't trying to suggest a competition of any kind, which is the way it come across."
Giuliani's explanation further angered his ground zero critics, prompting several to issue a statement demanding an apology.
"He is such a liar, because the only time he was down there was for photo ops with celebrities, with politicians, with diplomats," said deputy fire chief Jimmy Riches, who spent months digging for his firefighter son.
"On 9/11 all he did was run. He got that soot on him, and I don't think he's taken a shower since."
Harold Schaitberger, president of the International Association of Fire Fighters, a union that fiercely opposes Giuliani, said he doubted Giuliani misspoke.
"I think he was simply showing what his true character is — a self-absorbed, self-deluded promoter who got caught and is now just simply trying to backtrack," Schaitberger said.
A former deputy mayor, Joe Lhota, said the critics are politically motivated and wrong.
"They're taking their anger out in the wrong direction," Lhota said. "He was literally there four and five times a day; he did anything but run away.
"They're losing sight of the fact that this country, and this city, was attacked on that day by terrorists; it's their fault. Rudy Giuliani coordinated efforts in this city like no one had ever seen before."
Also Friday, Giuliani named another former deputy mayor, Rudy Washington, chairman of his campaign in New York City. Washington played a role in ground zero operations for weeks after Sept. 11 and received medical coverage for debilitating asthma and other health complications.