NEW YORK (CBSNewYork/AP) — The city’s Columbus Day parade stepped off Monday morning amid continued debate about the statues and the day honoring Christopher Columbus.

Even with the gloomy overcast skies and showers, no amount of rain was enough to stop the parade of red, white and green as spectators lined Fifth Avenue in what’s considered the world’s largest celebration of Italian-American culture.

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“It’s about pride in Italian-American heritage and showing pride in all they’ve done for the country and the world. So for me, it’s not really about Columbus but Italian-Americans,” said parade participant Thomas Vaughan.

Genny Marino and her friends were among the crowds watching the parade as it marches from 47th Street to 72nd Street.

“It’s my heritage,” Marino said. “That’s why I’m here. Not gonna miss this for a little rain drops.”

“We’re celebrating Italian migration to this country, we’re celebrating the American dream,” paradegoer Nick Mollenini of Yonkers said.

Among the 35,000 marching on Monday, was actor Frank Grillo, who said he’s humbled to be the NYPD’s Grand Marshall.

“It’s exciting to be Italian and a New Yorker today,” he said.

As CBS2’s Jessica Borg reported, for the first time at the parade there was a float celebrating Italian American authors including Brooklyn born actor and writer Tony Danza.

Trying to stay dry were marchers of the order Sons Of Italy — in historical garb that takes days to make.

“Because they are hand made costumes,” one marcher said.

Near the start of the parade, Timothy Cardinal Dolan said he enjoyed the tradition.

“Just a boost of faith, a boost of patriotism, a boost of pride that I feel as a New Yorker,” he said.

But for one Italian-American in attendance, it wasn’t the warmest of receptions, CBS2’s Janelle Burrell reported. Mayor Bill de Blasio spoke to reporters just before joining parade participants.

“You can debate the historic figure of Christopher Columbus but you can’t debate the contribution of Italian-Americans to this country,” de Blasio said. “That is beyond question.”

Many Italian-Americans felt as though the mayor betrayed them by allowing a city commission to determine whether Christopher Columbus statues in the city should be considered as symbols of hate.

“We’re very proud of our heritage, we’re going to continue to have our voice heard, and we respect all ethnicities. We do no celebrate him because of what he did negatively, we celebrate all the positive things that he did,” said Angelo Vivolo of the Columbus Citizens Foundation.

“Bill de Blasio should leave our statues alone,” said Morris Park resident Marisa Sputtoni. “Learn from history. Don’t destroy history.”

De Blasio, who was met with sporadic boos from the parade sidelines, defended the commission, WCBS 880’s Rich Lamb reported.

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“No one’s moving any statues. No one’s changing anything in the short term. We’re going to have a real public discussion about how we address issues of the past that should be surfaced and talked about in a responsible manner. I’ve said there are a lot of different solutions including something as simple as putting additional historical markers up,” the mayor said.

Those who believe the Columbus statues should come down cite Columbus’ mistreatment of Native Americans. There was a small group of protesters Sunday during a wreath-laying ceremony at the Columbus statue in Columbus Circle.

“It makes no sense that he should be a landmark,” one protester said. “It’s got to go.”

But those at the parade Monday say the statues and the celebrations must continue.

“The controversy is unfortunate because it’s really about peace and love and one people one city,” said Phyllis Perillo with the Columbus Citizens Foundation.

It’s not about taking anything away from Italian-Americans, said Cliff Matias, cultural director of the Redhawk Native American Arts Council.

“The conversation is Columbus,” he said. “If they’re going to celebrate Columbus, we need to celebrate the fact that we survived Columbus.”

Some area lawmakers have started a petition to keep the statue, many of them snubbing the mayor’s Italian-American heritage reception at Gracie Mansion.

“That statue has to remain at Columbus Circle,” said State Sen. Jeff Klein, (D-Bronx).

The mayor himself has not said what he thinks the fate of the statue should be. His spokesperson released a statement saying,  “there’s no plan to touch the Columbus statue.”

On Monday, he wouldn’t back down from his position.

“These issues have been bubbling up for years. We have to come up with a universal way to addressing them,” he told CBS2 Political Reporter Marcia Kramer.

Governor Cuomo said the statue will remain as long as he’s governor, and while he didn’t mention the mayor by name, his unhappiness with de Blasio’s actions were clear as a bell.

“This is divisive politics, and what I call definition by opposition. We want to define ourselves now by what we’re against. I believe in definition by affirmation, tell me what you’re for and what you believe. That’s how we bring people together,” Cuomo said.

The statue commission will meet for the first time this week, but the mayor would not say when or where.

Meanwhile, the Christopher Columbus statue in Columbus Circle remains under 24/7 watch by the NYPD.

Last month, vandals doused the hands of a Christopher Columbus statue in Central Park in blood-red paint and scrawled the words “hate will not be tolerated.”

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(© Copyright 2017 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)