WASHINGTON — The Supreme Court on Tuesday appeared ready to deal another setback to transgender people and uphold state laws barring transgender girls and women from playing on school athletic teams.

The court’s conservative majority, which has repeatedly ruled against transgender Americans in the past year, signaled during more than three hours of arguments it would rule the state bans don’t violate either the Constitution or the federal law known as Title IX, which prohibits sex discrimination in education.

More than two dozen Republican-led states have adopted bans on female transgender athletes. Lower courts had ruled for the transgender athletes who challenged laws in Idaho and West Virginia.

The legal fight is playing out against the backdrop of a broad effort by President Donald Trump to target transgender Americans, beginning on the first day of his second term and including the ouster of transgender people from the military and declaring that gender is immutable and determined at birth.

The justices are evaluating claims of sex discrimination lodged by transgender people versus the need for fair competition for women and girls, the main argument made by the states.

Justice Brett Kavanaugh, who coached his daughters in girls basketball, seemed concerned about a ruling that might undo the effects of Title IX, which has produced dramatic growth in girls and women’s sports. Kavanaugh called Title IX an “amazing” and “inspiring” success.

Some girls and women might lose a medal in a competition with transgender athletes, which Kavanaugh called a harm “we can’t sweep aside.”

The three liberal justices seemed focused on trying to marshal a court majority in support of a narrow ruling that would allow the individual transgender athletes involved in the cases to prevail.

A ruling for West Virginia and Idaho would effectively apply to the other two dozen Republican-led states with similar laws.

But the justices soon might be asked to decide about the laws in an additional roughly two dozen states, led by Democrats, that allow transgender athletes to compete on the teams that match their gender identity.

The outcome also could influence separate legal efforts by the Trump administration and others seeking to bar transgender athletes in states that have continued to allow them to compete.

In the Idaho case, Lindsay Hecox, 25, sued over the state’s first-in-the-nation ban for the chance to try out for the women’s track and cross-country teams at Boise State University in Idaho. She didn’t make either squad because “she was too slow,” her lawyer, Kathleen Hartnett, told the court Tuesday, but she competed in club-level soccer and running.

Becky Pepper-Jackson, a 15-year-old high school sophomore, was in the courtroom Tuesday. She has been taking puberty-blocking medication, has publicly identified as a girl since age 8 and has been issued a West Virginia birth certificate recognizing her as female. She is the only transgender person who has sought to compete in girls sports in West Virginia.

Pepper-Jackson has progressed from a back-of-the-pack cross-country runner in middle school to a statewide third-place finish in the discus in just her first year of high school.

Prominent women in sports have weighed in on both sides. Tennis champion Martina Navratilova, swimmers Summer Sanders and Donna de Varona and beach volleyball player Kerri Walsh-Jennings are supporting the state bans. Soccer stars Megan Rapinoe and Becky Sauerbrunn and basketball players Sue Bird and Breanna Stewart back the transgender athletes.