WASHINGTON — The Supreme Court raised doubts Wednesday about a law that bars the government from registering trademarks that are deemed offensive.

The justices heard arguments in a dispute involving an Asian-American band called the Slants that was denied a trademark because the U.S. Patent and Trademark office says the name disparages Asians.

The band says the 70-year-old law violates free speech rights. A federal appeals court ruled that the law is unconstitutional, but the government has appealed.

Justice Elena Kagan said it seemed like “a classic form of viewpoint discrimination” because the government appeared to favor positive names over those with negative connotations.

Justice Ruth Bader Ginsburg said the law wasn’t being enforced consistently, noting that the term Heeb was approved in one trademark application, but not in another. The term is considered offensive to Jews.

But the justices also seemed concerned that imposing no limits on trademark names would go too far.

“You want us to say that trademark law is just like a public park” where people can say whatever they want, Justice Anthony Kennedy told John Connell, lawyer for Slants founder Simon Tam.

A victory for the Oregon-based band would be welcome news for the Washington Redskins, embroiled in their own legal fight over the team name. The trademark office canceled the football team’s lucrative trademarks in 2014 after finding the word Redskins is disparaging to Native Americans.

At issue is a law that prohibits registration of marks that “may disparage … persons, living or dead, institutions, beliefs or national symbols.”

Tam has said his goal in choosing the band’s name was to reclaim a derisive slur and transform it into a badge of ethnic pride. But the trademark office said a term can be disparaging even if it’s meant to be used in a positive light. A federal appeals court sided with the band, ruling that the law violates the First Amendment.

The Obama administration wants the high court to overturn that ruling. Justice Department lawyer Malcolm Stewart told the justices that the law does not restrict speech because the band is still free to use the name even without trademark protection.

Stewart said the government was concerned about allowing trademarks for racial slurs, religious insults and other crude names that distract consumers and hinder commerce.

When Ginsburg asked if the phrase “Slants are superior” would pass muster, Stewart said it probably would.

Chief Justice John Roberts wondered why that wouldn’t be considered “disparaging of everyone else.”

“I’m concerned that your government program argument is circular,” Roberts said.

Connell, attorney for the Slants’ founder, said the First Amendment should allow trademark approval of any expression “no matter what.” But some justices seemed to think that argument went too far.

Kagan said “that just can’t be right,” noting the trademark law also has restrictions on marks that are libelous or cause confusion in the marketplace. She said the trademark program offers certain benefits “that the government doesn’t have to provide at all.”

Justice Stephen Breyer said the Slants are free to use the name in all kinds of ways, just not on the trademark itself.

“This is not a general expression program,” Breyer said. “It stops nobody from saying anything.”

Like the Slants, the Redskins say their name is meant to honor American Indians. But the team has spent years fighting legal challenges from Native American groups that say it’s a racial slur. A federal judge upheld the trademark office’s cancellation of the team’s name and the Redskins are appealing. The matter is on hold pending the outcome of the Slants case.

A ruling is expected by the end of June.