“The message today is clear: organized crime still exists in the city and the state of New York,” Mr. Cuomo said. “We like to think that it’s a vestige of the past. It’s not. It is as unrelenting as weeds that continue to sprout in the cracks of society.

“The second message, which is equally clear,” he added, “is that we will not rest until organized crime is a distant memory in New York.”

The arrests by the Federal Bureau of Investigation and investigators from several other agencies were coordinated with a sweep that netted 23 accused organized crime figures in Palermo, Sicily. Those charges are not directly linked to the New York arrests, but Italian officials who were in New York at the news conference said they were part of a new American-Italian strategy aimed at severing the close cooperative relationship between the Gambino family and the Sicilian mob.

Image Law enforcement officers escort people to be arraigned after the indictment of over 80 members of organized crime families on charges related to racketeering, conspiracy, extortion, theft, illegal gambling, loan-sharking and embezzlement in New York. Credit... Chip East/Reuters

In addition to Mr. D’Amico, Mr. Cefalu and Mr. Corozzo, the 80-count federal indictment charges three Gambino captains and three acting captains, who serve among the family’s midlevel managers, along with 16 dozen soldiers, officials said. A large number of family associates are also being charged.

The construction extortion aspects of the investigation, which began more than three years ago, focused on the trucking industry, which hauls away dirt excavated from major construction projects in and around the city, said Gordon S. Heddell, inspector general of the United States Labor Department. Several union officials were also charged in a scheme to steal union benefits. Mr. Heddell, whose office investigates labor racketeering, said his agents were instrumental in starting the investigation.

“This investigation exposed the alleged grip that the Gambino organized crime family has had over one of the largest construction markets in the United States, from small private projects to large scale public works contracts,” he said. “This involved the trucks that move construction material and debris throughout the entire New York City region  the cement that is poured to build house foundations out in Staten Island, the general contractors who are responsible for building condominiums over in New Jersey and even a proposed Nascar raceway.”