WASHINGTON (CNN) -- Former New City Mayor Rudy Giuliani defended his record with New York City firefighters Monday, three days after the president of the nation's largest firefighter union sharply criticized him for ordering to have Ground Zero debris removed before several firefighter's remains were recovered.

"I've been a big, big supporter of theirs' and friend of their's way before September 11th happened," Giuliani said in a press conference Monday. "I considered it my duty to be there when they were injured or hurt to make sure they got the best medical treatment possible."

"As far as any particular union is considered, they have lots of agenda items, but I think that I have a real bond with firefighters," he added "Unions -- some agree, some disagree, some have different agenda items."

In a draft letter to union members that surfaced Friday, International Association of Fire Fighters Union President Harold Schaitberger claimed Giuliani sought to shut down search and recovery efforts at ground zero before hundreds of firefighter's remains were found. "Many people consider Rudy Giuliani 'America's Mayor,' and many of our members who don't yet know the real story, may also have a positive view of him,'' Schaitberger wrote in the letter. "[The Union] wants to make all of our members aware of the egregious acts Mayor Giuliani committed against our members, our fallen on 9/11, and our New York City union officers following that horrific day."

The IAFF, which represents 260,000 firefighters and bills itself as non-partisan, endorsed Massachusetts Sen. John Kerry's presidential bid in 2004.

Watch Giuliani respond to firefighters' union criticism

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