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.