The Supreme Court agreed yesterday to decide whether the Federal Communications Commission can require cable television systems with at least 3,500 subscribers to designate one channel for use mainly by the public, educational and local governments.

The commission said the case presents a question "of great importance" about how it is to carry out its mission and "integrate new media into the national communication structure."

The nation has about 4,000 cable TV systems that enter 12.9 million homes - nearly 18 percent of the total equipped with television sets.

In the ruling to be reviewed, the 8th U.S. Circuit Court of Appeals held that in ordering access to cable TV systems - by 1986, in the case of existing ones - the FCC had exceeded the authority given it by Congress.

Finding from the record that the agency had taken "abitray and capricious" action, the appeals court said the access rules would violate the Constitution by denying freedom of speech and by taking property for public use without compensation due process of law.

Among those siding with the commission were the solicitor general of the United States the American Civil Liberaties Union and Consumers Union. The nonprofit consumer group said that expansion of "outlets for community self-expression and . . . the public's choice of programs . . . remains an objective of critical public importance."

The court took other actions: OCCUPATIONAL SAFETY

Seven of the nine justices voted to leave standing a 2-1 ruling that the occupational Safety and Health Act doesn't empower the Labor Department to prohibit employers from retaliating against workers for refusing to perform "particular tasks believed to represent an immediate danger to life or limb."

The action was a defeat for the department, which argued that the law prohibits a worker faced with a "cruel choice" between preserving his safety or his job. The ruling was handed down by the 5th U.S. Circuit Court of Appeals. The dissenters were Justices William J. Brennan, Jr. and Harry A. Blackmun. Defense Procurement

The court reinstated a one-court fraud indictment against Litton Systems Inc., which contends that "the whole program of defense procurement" has been put "in jeopardy."

A federal grand jury in Alexandria indicted Litton in April 1977, after prosecutors had cleared the matter with Attorney General Griffin B. Bell.

Judge Albert V. Bryan Jr. dismissed the indictment a few months later, alleging prosecutorial misconduct during preindictment negotiations with Litton.

Last April, however, the 4th U.S. Circuit Court of Appeals reversed Bryan. In doing so, it relied on a Supreme Court decision on plea bargaining that was handed down after Bryan's dismissal of the indictment. The Supreme Court declined to hear Litton's appeal of the 4th Circuit ruling.

THe case involves the Navy's denial of a $30 million claim arising from a nuclear submarine contract with Litton's Ingalls Nuclear Shipbuilding Division, and an agreement by both sides not to contest a compromise award of $16 million by the Armed Services Board of Contract Appeals.

The grand jury investigation began after the board held hearings, but before it announced the award. Because the government admittedly lacked sufficient evidence of criminal intent to establish guilt beyond a reasonable doubt, it let the gradn jury expire without seeking an indictment. But it continued to investigate.

Later, Assistant U.S. Attorney Frank W. Dunham Jr. proposed, and a Litton lawyer accepted, a formula to resolve the "intent question" both would petition the board to reopen the proceeding so the contract board could reconsider its award, the government wouldn't argue fraud in response to a Litton suit to increase the award, and the criminal investigation would be shut down.