WASHINGTON — A top supporter of Senator McCain is assailing Mayor Giuliani for making light of sleep deprivation as a form of torture, saying his joke is “an insult to all American soldiers who have had to endure real torture and mistreatment while in enemy hands.”

During a recent campaign swing in Iowa, Mr. Giuliani called the idea that sleep deprivation was torture “plain silly” and quipped that if that were the case, “I’m getting tortured running for president of the United States.”

The McCain campaign hit back yesterday, releasing a statement from the chairman of its Veterans Advisory Committee in New Hampshire, Sergeant Major Paul Chevalier, who demanded an apology from Mr. Giuliani. Major Chevalier also pointed to a close friend of the Arizona senator, Lieutenant Colonel Orson Swindle, who was subject to sleep deprivation while a prisoner of war in North Vietnam. Lieutenant Colonel Swindle, Major Chevalier said, “can personally assure Mayor Giuliani that the experience was far more severe than the loss of sleep he experiences as a candidate.”

Mr. McCain himself was tortured repeatedly during his five years as a prisoner of war during Vietnam, and he has been the most explicit among the leading GOP candidates in condemning interrogation techniques that many people consider torture, such as waterboarding.

He has criticized the former mayor for his unwillingness to denounce waterboarding, which involves simulated drowning, and for comparing the debate over interrogation of terrorists to his experience questioning mob leaders as a federal prosecutor. “When someone says waterboarding is similar to harsh interrogation techniques used against the mafia in New York City, they do not have enough experience to lead our military,” Mr. McCain said in Iowa on Sunday, according to the Boston Globe. On Monday, he called Mr. Giuliani’s comment about sleep deprivation “flip.”

In response, the Giuliani campaign said Mr. McCain couldn’t take a joke. It released a statement from its senior military adviser, Admiral Robert Natter, who pointed to Mr. McCain’s use of humor on the campaign trail and his frequent appearances on Comedy Central’s “The Daily Show.”

“I think it’s a little over-the-top to imply that Mayor Giuliani intended to insult anybody, considering the senator’s own noted history of levity,” Admiral Natter said.

Mr. McCain’s sense of humor has also caused him problems during the campaign, most notably earlier this year when he responded to a question about Iran by singing, “Bomb, bomb, bomb, bomb, bomb Iran” to the tune of the Beach Boys hit “Barbara Ann.”