The Supreme Court yesterday signaled its readiness for a possible relaxation of one of the most controversial requirements of criminal law: the rule forbidding use at a trial of evidence illegally seized by police.

The justices, over three bitter protests, agreed to consider establishing a "good faith" exception to the rule for occasions when police "reasonably" believe they are acting legally when conducting a search even though it later turns out to have been illegal in some respect.

Such an exception to what is called the "exclusionary rule" is a prime goal of conservative critics of criminal justice procedures, including President Reagan. These critics have long argued that too many otherwise solid cases are being thrown out because of the rule.

The issue has arisen in previous cases at the court. But the unusual way in which the court acted yesterday suggested that the supporters may finally have enough votes. The court, over the three dissents, ordered a previously argued criminal case to be reargued with the addition of the "good faith" issue, even though it had not been raised earlier in the case. That action required at least five votes -- a majority -- as opposed to the four votes required for a simple grant of review.

The case, Illinois vs. Gates, began in May, 1978, when police in Bloomingdale, Ill., received an anonymous tip that Lance and Sue Gates were about to make a major drug buy in Florida. Police corroborated some of the tip, such as the address of the couple, obtained a search warrant from a judge and allegedly seized from the couple's home and car 350 pounds of marijuana, weapons, ammunition, drug paraphernalia and cocaine.

The Illinois courts threw the evidence out on the grounds that the information used to obtain the warrant -- the anonymous tip -- was insufficient and the warrant thus invalid. Illinois appealed.

Illinois now also argues that the evidence should be admitted because the police, armed with what they thought was a valid warrant, acted in the "good faith" belief that their search was legal.

In an interview, Yale Kamisar, a University of Michigan Law School professor and an expert on the exclusionary rule, said that if ever there were a case where a good-faith exception might be acceptable to the court, yesterday's was it.

The Bloomingdale police duly applied for a warrant, he said. "They did not mislead, and they were honest." In most similar cases, Kamisar said, the police have not even bothered to obtain a warrant.

"It sounds like the court finally decided to take the plunge and address themselves to the question in a context that is most favorable for a reasonable good-faith modification," he said.

The exclusionary rule was formulated by the court in the '60s as a deterrent to illegal searches. If illegal evidence taken in violation of the Fourth Amendment's search and seizure restrictions could be admitted, the police would have no incentive to obey the law, the court reasoned.

Recent studies show that only 1 to 2 percent of federal criminal cases fail because of the rule. Critics contend that is too many.

The court's action in the Illinois case was exceptional. Illinois had never raised the good-faith question in the lower courts and had, in fact, been rebuffed last spring by the Supreme Court in an attempt to add it. Higher courts are generally not supposed to consider issues not raised in the courts below. The Supreme Court has been reinforcing that policy recently, particularly when criminal defendants have attempted to raise new issues.

The justices accepted the Illinois case for review last spring and heard arguments Oct. 13 from lawyers on both sides. Not a word about a good-faith exception came up during the argument. Instead, they focused on the validity of the warrant.

Yesterday, however, the court said the case would be reargued with the addition of the question as to whether it should "not require the exclusion of evidence obtained in the reasonable belief that the search and seizure at issue was consistent with the Fourth Amendment."

Justice John Paul Stevens, joined by Justices William J. Brennan and Thurgood Marshall, called the action "a flagrant departure" from "settled practice" that "raises serious questions."

Also yesterday, the court agreed to hear another controversy involving regulation of nuclear power plants. The justices said they would review a decision by the U.S. Court of Appeals here requiring the Nuclear Regulatory Commission to consider in detail the environmental impact of nuclear waste storage and disposal before allowing plant operation.

The case, U.S. Nuclear Regulatory Commission et al vs. Natural Resources Defense Council, et al, etc., is a sequel to a 1978 Supreme Court decision striking down the same judge -- David L. Bazelon -- in the same case, then called the "Vermont Yankee" case. The case went back to Bazelon, who stuck to his view in spite of a strongly worded denunciation of his judgment.

In addition to the power plant question, the case is an important test of the authority of the courts to override decisions by administrative agencies.