Relatives of firefighers who died in the attacks say that Giuliani pushed for a quick cleanup of Ground Zero at the expense of finding the remains of those who died.
"Virtually the whole thing goes back to him with the radios," Jim Riches, a deputy fire chief whose son was killed on September 11, says in the video.
"He's the guy on the top, and he's the guy you yell at," he said.
"He takes the hit. And my son is dead because of it."
But many of Giuliani's supporters called the video a "mockumentary".
Lee Ielpi, a former New York firefighter whose son died on September 11, and Richard Sheirer, called the video a "disgrace" and said it was full of "half-truths".
Ielpi refuted the claims made in the tape that workers searching for remains were pulled from the rubble, arguing that Giuliani allowed some workers to return.
Similarly, Sheirer said it was not the radios that did not work but rather a high-rise signal transmission system that was not functioning in one of the towers but which worked "perfectly" in the other.
"I was there. I saw it. I experienced it," said Ielpi, who worked at Ground Zero for the nine-month cleanup operation. "I'm not going to let lies like this go."
The 13-minute video was being distributed to the union's 280,000 members, to the media and online.
Steve Cassidy, president of the uniformed firefighters association, which represents about 9,000 firefighters, said: "This image of Rudy Giuliani as America's mayor - it's a myth."