WASHINGTON - The Supreme Court has rejected a long-shot appeal from the Washington Redskins challenging a law that bars offensive trademarks. But the justices could still resolve the same issue in another case the court took up last week.

The court on Monday turned away an unusual request to hear the team’s case even before a federal appeals court has weighed in. The Redskins are appealing the government’s decision to cancel its trademarks over concerns the name disparages American Indians.

In a separate case, the justices will decide whether the trademark law violates the First Amendment. That case involves The Slants, an Asian-American rock band that was denied a trademark​ on the ground that it disparages Asians.

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A federal appeals court sided with the band. The ruling said the band had the right to trademark protections even if some people were offended by the name of the band. The Redskins wanted both cases heard together.

The team’s appeal has not even been heard yet by a federal appeals court in Richmond, Virginia. In an unusual request, the team asked the Supreme Court to intervene before the lower court acts. The high court almost never grants such requests.

The Slants say their goal in choosing the name was to transform a derisive term about the shape of Asian eyes into a statement of ethnic and cultural pride. The Redskins have similarly claimed their name honors American Indians, but the team has faced years of legal challenges fromIndian groups that say the name is racist​. The team has also come under intense public pressure to change the name, though owner Dan Snyder has refused.

In the band’s case, a divided federal appeals court in Washington, D.C., struck down a portion of the 70-year-old federal trademark law. The court’s majority said the First Amendment protects “even hurtful speech that harms members of oft-stigmatized communities.”

The Obama administration is urging the high court to overturn the ruling. The government says the law “simply reflects Congress’ judgment that the federal government should not affirmatively promote the use of racial slurs and other disparaging terms by granting the benefits of registration.”

The administration also argues that the law does not restrict speech because the band is still free to use the name even without trademark protection.

The Slants and the Redskins can continue using their preferred names even without trademark protection. But a trademark confers certain legal benefits, including the power to sue competitors that infringe the trademark. For the Redskins, the team could lose millions if it can’t block the sale of counterfeit merchandise.