By Hilary Russ

NEW YORK (Reuters) - The four major U.S. professional sports leagues could reap a combined $4.2 billion annually as a result of legal sports betting, most of it indirectly from increased fan engagement, according to a casino industry survey released on Thursday.

The findings could fuel a long-simmering feud between the gaming industry and American sports leagues, who want a share of the gambling revenue as U.S. states begin to legalize sports betting.

The survey showed leagues stand to benefit even without taking a cut of wagers. The National Football League is likely to make the most, with a projected $2.33 billion of additional annual revenue, according to the study seen by Reuters. The rest would go to Major League Baseball, the National Basketball Association and the National Hockey League.

The Nielsen Sports survey was commissioned by the American Gaming Association (AGA), which represents the casino industry. The NBA and MLB and declined to comment. The NFL and NHL did not reply to requests for comment.

For years, the leagues fought states' efforts to legalize sports betting, arguing it would lead to game fixing.

But in May, the U.S. Supreme Court threw out a federal ban against sports betting, paving the way for any state to legalize, regulate and tax the activity.

Since then, the leagues have sought to glean a portion of the coming windfall to help them fund additional integrity measures. They also have argued that they deserve a portion of wagers because there would be nothing to bet on without their players, stadiums and games.

Major League Baseball has said it wants 1 percent of the total amount of money bet as an "integrity fee."

Lawmakers in New Jersey, the first major state outside of Nevada to roll out sports betting, flatly rejected that idea.

At last week's annual Global Gaming Expo in Las Vegas, tensions flared when Kenny Gersh, an MLB executive vice president, told a panel the integrity fee should be called a "royalty" and that leagues had lowered their request to 0.25 percent.

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"You want a cut of the revenue without any of the risk," shot back fellow panelist Sara Slane, the AGA's senior vice president of public affairs.

"We have to go through a regulatory process. We invest billions of dollars in buildings and our licenses," she said. "You want us to take that risk, pay you, and then you're going to benefit on the back end as well."

The AGA study found that $596 million of leagues' total increased annual revenue would come from gaming services spending on television advertising, $267 million from sponsorship deals with the sports betting industry and $89 million from data and video revenue.

But the study projected that the bulk of the projected windfall would come if more fans, attracted by betting, attend games or watch them. Nearly $3.3 billion is tied to those indirect revenues, including media rights and more merchandise and ticket sales.

For the NFL alone, indirect revenues could grow 13.4 percent to $14.8 billion of annual revenue, the report said.

The study has a margin of error of 3 percentage points and surveyed more than 1,000 adult sports fans and self-identified bettors nationwide, asking how a national legal market would affect sports consumption habits.

The national market would need to include at least 100 million people for the leagues to fully benefit, Nielsen estimated.

(Reporting by Hilary Russ, Editing by Rosalba O'Brien, Bill Berkrot and David Gregorio)