NEW YORK (AP) _ The reputed head of the Genovese crime family and 14 others have been charged with manipulating the Teamsters union and controlling the city's high- rise construction industry, along with gambling, extortion and murder conspiracy.

An 88-page, 29-count indictment issued Friday charged the organization, allegedly run by Anthony ''Fat Tony'' Salerno, helped elect and control the former head of the International Brotherhood of Teamsters, Roy Williams.

The indictment ''may very well be the most comprehensive yet brought'' in the federal campaign against organized crime, U.S. Attorney Rudolph W. Giuliani said.

It ''shows how organized crime can subvert the free enterprise system. The victims are everywhere,'' said John L. Hogan, assistant FBI director in New York.

It was the latest indictment of key figures in New York's five La Cosa Nostra families. Salerno, 74, of Rhinebeck, already faces charges that he participated in a crime ''commission'' that directed the families' activities.

The grand jury charged that Milton Rockman, a reputed associate of the Cleveland organized crime family, met with Cleveland, Chicago and New York crime bosses to engineer Williams' election as Teamsters president in 1981. The bosses allegedly influenced local Teamsters leaders to support Williams.

Williams was forced to resign the Teamsters presidency in 1982 after his conviction for conspiracy to bribe a U.S senator. He is serving a 10-year prison sentence. In November, Williams testified that he took monthly payoffs from a reputed Kansas City, Mo., crime boss.

The indictment said Genovese members sought through bribes to control two New York Teamster locals, 560 and 282, and controlled the District Council of the Cement and Concrete Workers, Laborers International Union.

Salerno and others allegedly used their union influence to enforce control of the Manhattan construction industry, the indictment said. It charged that they rigged bids for concrete subcontracts worth more than $2 million, then threatened to halt deliveries to reluctant construction site managers.

''You're talking about millions and millions of dollars in some of the most important construction projects in Manhattan in the last five years,'' Giuliani said. The indictment named 16 of them.

Two others indicted were identified as Genovese associates, Nicholas Auletta, 53, of Pelham Manor, president of S&A Concrete Co., and Edward J. ''Biff'' Halloran, 45, of Pelham, an operator of concrete firms including Transit-Mix Concrete Corp..

Halloran and Auletta were named in a federal antitrust suit last year that charged contractors had rigged concrete bids on major construction projects since 1978.

That suit said $3.3 million was added to the cost of concrete for the Jacob K. Javits Convention Center in Manhattan and estimated total overcharges in the industry were $40 million to $50 million a year.

The indictment also charged the Genovese operatives ran an extensive illegal gambling operation and killed ''individuals who posed a threat.'' It alleged conspiracies to murder two men, one of whom was killed.

Rockman was charged only with one count of wire fraud; the others were charged with racketeering and other charges. Giuliani said prosecutors would seek to seize assets gained by criminal activity.

Two other mob cases are under way in federal court in Manhattan: the ''Pizza Connection'' heroin smuggling case, involving reputed members of the Bonnano crime family; and a case charging reputed Colombo family members with racketeering.