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The push for a ticker-tape parade down the Canyon of Heroes for Iraq veterans is gaining new traction after New York City hosted its blow-out celebration for the New York Giants -- a festival that raised immediate questions about why the country is not extending the same honor to returning soldiers.

Lawmakers representing New York, and at least one national veterans group, are renewing their call for a parade -- though the pushback appears to be coming not from New York but from Washington.

"We think the mayor is actually somewhat on board -- and we think the stumbling block might be the White House and the Pentagon," Joseph Borelli, chief of staff to New York Councilman Vincent Ignizio, told FoxNews.com.

Mayor Michael Bloomberg has said the Pentagon is uneasy about a parade, as long as U.S. troops are still in harm's way.

Ignizio told MyFoxNY.com on Wednesday that Bloomberg wants a parade, "but he's saying the Pentagon and the Obama administration is saying that they don't want to do it until after the Afghanistan war, which doesn't make sense."

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Ignizio cited past examples, such as during World War II, when troops were honored with celebrations despite the fact that the war was not over. Ignizio said the delay might be "somewhat political," out of concern that the administration does not want a "mission accomplished" moment.

"This is not about spiking the football," Ignizio said. "This is just about saying thank you."

Rep. Michael Grimm, R-N.Y., who has pushed vociferously for a parade, told FoxNews.com he understands the concern about the timing. He said the troops who are home deserve the honor, but noted that some Iraq veterans are doing another tour of duty in Afghanistan.

"That's my only trepidation," Grimm said. "I would want all of them to be able to have that honor."

Grimm, a veteran of the first Iraq war, participated in the parade after that conflict -- he called it "one of the highlights of my life."

Grimm said he's "torn" over whether the country should green-light a parade in the near-term, or wait until all the Iraq vets are home.

"I wouldn't want anyone to miss that," Grimm said, adding: "Everyone's trying to do the right thing. ... It's not partisan. It's not politics."

As Ignizio and his colleagues on the council push for a parade soon, the director of Iraq and Afghanistan Veterans of America is doing the same.

Paul Rieckhoff, in a column on his group's website, questioned why the idea of a parade was meeting "resistance."

"For the Mayors of New York and Boston: are you really okay with your football teams getting ticker tape parades and not your new veterans? I am as big a fan as they come, but why do the Giants get a parade in the Canyon of Heroes and not our nation's military? If that does happen, what does that say about us as a society and our priorities?" Rieckhoff wrote.

His group is also circulating a petition.

The city of St. Louis already has hosted one parade for Iraq war veterans. More than 1 million Americans served in the Iraq war; more than 4,200 U.S. servicemembers lost their lives in the war.

Bloomberg said on NBC's "Meet the Press" on Sunday that the Pentagon had asked New York to "postpone" a parade.

"I think I'll leave it up to the military experts and the Pentagon to decide when they think it's appropriate, and then New York will give them a parade like we've never done before to say thank you for everything they've done," Bloomberg said.

Grimm was confident Iraq war veterans will eventually walk the Canyon of Heroes.

"One way or the other ... there's going to be a parade. And I'll fight with every breath in my body to make sure it happens," Grimm said.

FoxNews.com's Judson Berger contributed to this report.