The Supreme Court, stepping into a power struggle between the Federal Communications Commission and local governments, agreed yesterday to decide the extent of the FCC's authority to regulate the quality of the signals transmitted by cable television operators.

The dispute, part of widespread litigation over various parts of the Cable Communications Policy Act of 1984, centers on whether Congress wanted to allow the FCC to continue its longstanding policy of preempting local government regulation of cable signal quality.

A federal appeals court panel here ruled 2 to 1 last March that the FCC was right to conclude Congress intended to grant the commission that authority. Several cities, along with the National League of Cities, appealed, saying that a proper reading of the act would show that Congress never intended to allow the FCC to stop local governments from adopting their own standards to supplement FCC guidelines that are "so minimal that they amount to no guidelines at all."

The cities said they were concerned with what they felt was "the erosion of their authority to deal with cable systems and to enforce negotiated franchise provisions."

Montgomery County, joined by three cities, filed a brief in the case against the FCC position. Nicholas P. Miller, an attorney for the county, said it has a contract requiring cable operators to use state-of-the-art technology in transmitting signals. The county "was concerned that {if the FCC position were upheld} the contract could be largely unenforceable if they cannot impose those technical standards," Miller said.

Miller said yesterday's decision by the court to hear the case, City of New York v. Federal Communications Commission, "is encouraging because it suggests the possibility that the court disagrees with the FCC's claimed authority to prevent effective local enforcement of cable signal quality."

But the FCC, in its brief, argued that its preemption policy was needed to "prevent any adverse impact on the growth of cable television because of the imposition of overly burdensome technical requirements at the local level" and because it felt there "should be a national policy in the technical area," not one varying from city to city.

The FCC said the appeals court correctly interpreted congressional intent in passing the 1984 act. The appeals court said Congress acted "against the backdrop of the commission's preexisting preemption regulation without criticizing that regulation." As a result, the court said that "we infer that Congress endorsed it, except where the Cable Act explicitly or implicitly modified its provisions."

The Supreme Court is expected to rule in the case by July.

The court also agreed to decide whether the Reagan administration could stop regulating some natural gas prices. The justices said they would take up the issue, involving the Natural Gas Policy Act of 1978, in Federal Energy Regulatory Commission v. Martin Exploration and Public Service Commission of New York v. Martin Exploration.

In a third case, the justices said they would hear an appeal by an Amtrak engineer who claimed he was improperly denied representation by his union at a disciplinary hearing that resulted in his suspension from work for 30 days. The court will likely hear oral arguments in the case, Landers v. National Railroad Passenger Corp., this spring.