ASHINGTON, March 29 — The Supreme Court agreed on Monday to settle one of the most disputed questions in civil rights law: how to win an age discrimination case in the absence of proof that an employer deliberately singled out older workers for unfavorable treatment.

The issue in a case brought by a group of older police officers in Jackson, Miss., is whether the federal law against age discrimination covers policies that do not relate directly to age but that have a disparate impact on older workers.

In this case, the older officers are trying to show that new wage scales, intended to make the pay for more recently hired officers more competitive with other police departments in the region, had the effect of giving proportionately smaller increases to the more senior officers. The 30 plaintiffs in the lawsuit are all at least 40 years old, the age at which coverage under the Age Discrimination in Employment Act begins.

Both the Federal District Court in Jackson and the United States Court of Appeals for the Fifth Circuit, in New Orleans, ruled for the city on the ground that the law requires proof of "disparate treatment," meaning intentional discrimination. Neutral policies that have a differential impact on different age groups are not covered by the law, the appeals court said in a 2-to-1 ruling last November.

Other federal appellate circuits have reached the opposite conclusion, and the legal dispute has been raging for years. Two years ago, the Supreme Court tried to resolve it in a case brought by older workers against the Florida Power Corporation. But the justices dismissed that case without a decision after the argument raised questions about whether the company policies that were the basis for the complaint actually existed.

The Jackson police officers' appeal, Smith v. City of Jackson, No. 03-1160, citing federal labor statistics, said that 70 million employees, nearly half the civilian labor force, are at least 40 years old and are therefore within the age-discrimination act's coverage.

For more than 20 years, the Equal Employment Opportunity Commission has had a regulation on its books that adopts the broader "disparate impact" interpretation of the law. But when the issue was before the Supreme Court two years ago, the Bush administration did not defend the regulation and filed no brief in the case.

Its reticence no doubt reflected the fact that across the entire range of employment discrimination law, the ability of judges to impose remedies when plaintiffs have not proven deliberate discrimination is under sustained attack from employer groups and conservative legal organizations. When the earlier case was pending, one prominent conservative group, the National Legal Center for the Public Interest, published a study of discrimination law that said that the disparate-impact approach "deserves to be attacked at every opportunity."

Interpreting Title VII of the Civil Rights Act of 1964, which bars employment discrimination on the basis of race and sex, the Supreme Court ruled that suits can be brought under a disparate-impact theory without proof of discriminatory intent. Congress ratified that understanding when it amended Title VII in 1991.

Congress used Title VII as a model when it passed the age discrimination law in 1967, and the argument has been that it should be interpreted in the same manner. But there is one textual difference, as Chief Judge Carolyn Dineen King of the Fifth Circuit pointed out in her majority opinion in the new case before the Supreme Court. The age discrimination law offers employers an exemption "where the differentiation is based on reasonable factors other than age."

Judge King, joined by Judge Patrick E. Higginbotham, said that this phrase "appears to preclude a disparate impact theory of liability" because it "appears to serve as a safe harbor for employers who can demonstrate that they based their employment action on a reasonable non-age factor, even if the decision leads to an age-disparate result."

In a dissenting opinion, Judge Carl E. Stewart said that Congress intended in the age discrimination law to offer the same broad protection as it did in Title VII. Both laws, he said, reflected the recognition "that in a complex society, not all discrimination is apparent or overt" but will often be "subtle and concealed," lacking overt proof of a discriminatory motivation.

In a separate case on Monday, the Supreme Court agreed to decide whether criminal convictions obtained in the courts of foreign countries count as convictions that make it illegal for a convicted felon to own a gun. The federal law at issue, usually referred to as Section 922, applies to a person "who has been convicted in any court" of a crime punishable by a prison term of more than one year. The legal question is what the statute means by "any court," and the federal appeals courts have disagreed on the answer.

The case the justices accepted, Small v. United States, No. 03-750, is an appeal by a man who had been convicted of a firearms offense in Japan in 1994. Four years later, he bought a handgun in Pennsylvania from a licensed dealer and filled out a federal form answering "no" to the question of whether he had been "convicted in any court" of a crime with more than a one-year sentence.

The man, Gary S. Small, was later charged with making a false statement along with illegal gun possession. He argued that the indictment should be dismissed because "any court" did not apply to the Japanese conviction. The United States Court of Appeals for the Third Circuit, in Philadelphia, rejected that contention. While defending that judgment, the Justice Department agreed with Mr. Small that the Supreme Court should accept the case in order to resolve the dispute. The department noted that while the issue came up infrequently, it was important to have a uniform national rule.