WASHINGTON (Reuters) - Republican presidential candidate Rudy Giuliani came under attack on Friday from Democratic rival John Edwards for saying he spent as much time if not more at the site of New York's destroyed World Trade Center than rescue workers.

The clash highlighted the continued importance of the September 11 attacks to U.S. presidential politics as Giuliani tries to use his record as former New York City mayor to help him get into the White House.

The group 9-11 Families, which represents some of those rescue workers, demanded an apology, saying, "Rudy Giuliani has insulted all September 11 first responders, family groups and especially those of us who are battling life-threatening illnesses with his delusional statement."

In a visit to Cincinnati on Thursday, Giuliani told reporters that no one did more for firefighters killed in the attacks and their families than he did and that he raised millions on their behalf.

"Every single penny of the $227 million went to the families," Giuliani said. "This is not a mayor or governor or president who was sitting in an ivory tower."

"I was at Ground Zero as often, if not more, than most of the workers," he said.

The Edwards campaign issued a statement from its national chairman, former Michigan Democratic Rep. David Bonior, who said, "Evidently, Rudy Giuliani has taken a break from reality."

WASHINGTON - Republican presidential hopeful Rudy Giuliani said Friday that he misspoke when he said he spent as much time, if not more, at ground zero exposed to the same health risks as workers combing the site after the Sept. 11 attacks.

"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.