The New York Giants are showered with confetti and greeted by throngs as they are feted with the city’s most storied honor: a parade through its Canyon of Heroes.

But all the fanfare — the parade this week is the fourth since 2000 to honor a sports team — has touched off anger and unease among some returned Iraq veterans, who are eagerly awaiting their own recognition.

“Everybody recognizes that the Giants deserve a parade,” said Paul Rieckhoff, founder and executive director of Iraq and Afghanistan Veterans of America. But, he added, “If a football team gets a parade, shouldn’t our veterans?”

Mayor Michael R. Bloomberg, who has long expressed his regret that the United States did not do a better job honoring veterans of the Vietnam War in the 1970s, has cited advice from the Pentagon in deciding it was not appropriate to hold a parade while American soldiers are still fighting in Afghanistan.

But a growing coalition of veterans, elected officials and other public figures are disagreeing, saying it is time to celebrate the men and women who served in Iraq.

Leslie H. Gelb, the president emeritus of the Council on Foreign Relations, a former correspondent for The New York Times and a board member of the Iraq and Afghanistan Veterans of America, called the Pentagon’s position “supercilious sensitivity” and “Washington-think.”

“Celebrating the Iraqi vets doesn’t negate a future celebration for the Afghan vets or deny that we’re still at war,” Mr. Gelb said, adding that “if we had to wait to honor our servicemen and women until wars were over, that would take a long time.”

And former Mayor Edward I. Koch, who in 1981 was the host of a “ticker-tape” parade for American hostages released from Iran over the objection of Alexander M. Haig Jr., then secretary of state, said he thought a parade for Iraq veterans was important and timely. Mr. Koch, who also hosted a belated parade for Vietnam War veterans in 1985, said the Pentagon was making “a political decision” that he termed “ridiculous.”

“It’s not premature,” he said. “I believe that a parade is required, is necessary, and New York City is the place to have it.”

But the Defense Department, noting that American soldiers are still fighting in Afghanistan, says it is too soon for a celebration with the recognition and symbolism of a New York City parade.

Col. David Lapan, a spokesman for Gen. Martin E. Dempsey, the chairman of the Joint Chiefs of Staff, said, “We simply don’t think a national-level parade is appropriate while we continue to have America’s sons and daughters in harm’s way.”

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