WASHINGTON — The Supreme Court on Friday agreed to resolve a dispute between television broadcasters and Aereo, an Internet start-up that the networks say threatens the economic viability of their businesses.

The case has far-reaching implications for the big broadcasters, jeopardizing an increasingly vital stream of income known as retransmission fees, the money paid to networks and local stations for the right to retransmit their programming. At least two of the networks, CBS and Fox, have already said they would consider abandoning broadcasting over public airwaves altogether and becoming pay cable channels if the Supreme Court were to decide in favor of Aereo.

There are huge revenue streams at risk for the broadcasters. The research firm SNL Kagan has estimated that together they will take in more than $4 billion in retransmission fees from cable and satellite companies in 2014, a total that Kagan estimates will grow to more than $7 billion within the next four years.

Aereo uses an array of small antennas to stream over-the-air television signals to subscribers, allowing them to watch programs on their smartphones, tablets and computers. The broadcasters say this amounts to theft of their content and violates copyright laws. Aereo responds that it is merely helping its subscribers do what they could lawfully do since the era of rabbit-ear antennas: watch free broadcast television delivered over public airwaves.

Chet Kanojia, founder and chief executive of Aereo, a start-up that retransmits network television shows to subscribers. Bebeto Matthews/Associated Press

Both Aereo and the networks said Friday that they welcomed the court’s decision to hear the case.

“We believe that Aereo’s business model, and similar offerings that operate on the same principle, are built on stealing the creative content of others,” CBS said in a statement. “We are pleased that our case will be heard and we look forward to having our day in court.”

Fox Broadcasting, ABC, NBC, Univision and PBS also supported the court’s decision to decide the issue.

Aereo’s chief executive, Chet Kanojia, said in a statement that the company hoped from the beginning “that this case would be decided on the merits and not through a wasteful war of attrition.”

“We look forward to presenting our case to the Supreme Court and we have every confidence that the court will validate and preserve a consumer’s right to access local over-the-air television with an individual antenna,” Mr. Kanojia said.

The “war of attrition” that Aereo referred to was the prospect that the company would have to face off against lawsuits in innumerable jurisdictions as local broadcasters all over the country sued to prevent the service from starting up. That would have presented a prohibitive cost for Aereo.

But the broadcasters also sought a quick resolution, hoping for a judgment that would forestall not just Aereo but also the cable and satellite companies who pay hundreds of millions each year for what is known as “retransmission consent.”

Aereo itself is not as worrisome to the networks as the possibility that its technology would be co-opted by cable and satellite companies looking to avoid paying those fees.

DirecTV, Charter Communications, and Time Warner Cable, which just lost an ugly retransmission-fee showdown with CBS, have all indicated they would consider a similar approach to Aereo’s if the service were declared legal.

Aereo was started by Mr. Kanojia in 2012, with the backing of Barry Diller, the chairman of the media conglomerate IAC/InterActiveCorp and formerly the co-founder of the Fox network. Available at first in New York City, the service has since expanded to other cities like Atlanta and Boston.

The company has been celebrated by so-called cord-cutters, television consumers seeking ways around ever-increasing cable and satellite bills. In his statement, Mr. Kanojia also outlined another of Aereo’s lines of defense: that a decision against it would damage innovation in areas like cloud computing and cloud storage — services that enable users to create a kind of DVR in the sky, where hours of programming can be stored.

David Bank, a media analyst for RBC Capital Markets, said in an interview Friday, “This is a watershed moment,” but he added that the real significance would not be known until the court made “a definitive declaration” of whether Aereo was a legal business.

If Aereo were to win, he said, “It would be very disruptive to the television ecosystem.”

Last April, Chase Carey, the president of 21st Century Fox, the parent of the Fox network, said at a convention of broadcasters that the company would consider drastic action, like shifting from broadcast to cable distribution, if the Aereo service was found legal. “We can’t sit idly by and let someone steal our signal,” Mr. Carey said. “We like the broadcast business, and if we can affirm our rights, that is a path we prefer to pursue.” He said that the “dual revenue stream” from both advertising and retransmission fees was vital for the future of the network.

Leslie Moonves, the president of CBS, also said switching to cable was an option for the future.

Some analysts have dismissed the suggestion as posturing in the legal battle, as well as an attempt to influence regulators. But Mr. Bank said he believed the broadcast networks would “likely have to undergo something of an evolution to become cable networks.”

The case rests on a part of the copyright law that requires copyright owners’ permission for “public performances” of their work. The law defines such performances to include retransmission to the public. The networks say Aereo’s service violates that provision.

Aereo says it is not covered by the provision. Because it assigns individual antennas to every viewer, Aereo contended that its Internet streams are not public performances under the copyright law. That means, it argued, that it has no obligation to pay so-called retransmission consent fees to local stations.

In its petition to the court, the broadcasters called that position nonsensical.

“For example, when tens of thousands of Aereo subscribers all simultaneously watch the same broadcast of the Super Bowl using Aereo, Aereo is not publicly performing the Super Bowl,” the petition said, mocking Aereo’s argument. “It is merely making tens of thousands of simultaneous ‘private’ performances to its subscribers.”

In its brief to the Supreme Court, Aereo said it merely sought to make good on the original deal between broadcasters and the government.

“The essential bargain that petitioners made to obtain, for free, public spectrum worth billions of dollars was that, once they have broadcast their programming, consumers have a right to receive and to view that programming using an antenna and to copy that programming for their personal use,” the brief said.

A divided three-judge panel of the federal appeals court in New York in April ruled for Aereo. In dissent, Judge Denny Chin wrote that the service was “a Rube Goldberg-like contrivance, overengineered in an effort to avoid the reach of the Copyright Act and to take advantage of a perceived loophole in the law.”

In September, the broadcasters won a preliminary injunction in Federal District Court in Washington against a similar antenna-based service, Film On, based on copyright infringement.

The case is ABC Inc. v. Aereo, No. 13-461.

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