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.

Democratic presidential hopeful John Edwards speaks at the Visible Vote '08 Presidential Forum sponsored by the Human Rights Campaign Foundation and broadcast on the Logo Network in Hollywood August 9, 2007. REUTERS/Mario Anzuoni

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.”

“It is outrageous for Giuliani to suggest, in any way, shape or form that he did more at Ground Zero or spent more time there than the brave first responders who worked tirelessly around the clock for many months during the rescue and recovery operation,” Bonior said.

Thousands of rescue workers who combed through the debris of the collapsed World Trade Center towers have developed health problems from breathing in the dust and fumes from the buildings.

Giuliani admitted on Friday in an interview with talk radio host Mike Gallagher, “I probably could have said it better.”

“What I was trying to say yesterday is that I empathize with them because I feel like I have that same risk,” Giuliani said.

He said he was not suggesting he was competing with the rescuers, while admitting it came across that way.

“Gosh almighty, I was there often enough, even though they were there, people there more and people there less, but I was there often enough so that every health consequence that people have suffered, I could also be suffering,” he said.

Giuliani’s communications director, Katie Levinson, lashed out at the Edwards camp for its attack.

“For John Edwards to lecture Rudy Giuliani about September 11 is laughable at best. This is, after all, the same guy who thinks the ‘war on terror’ is simply a bumper sticker,” she said.