WASHINGTON — The Supreme Court on Wednesday seemed willing to put more bite into a law that requires public schools to help learning-disabled students.

Most of the justices indicated during arguments that school districts must offer more than the bare minimum of services to children with special needs. But they struggled over how to clarify the law without inviting even more litigation between frustrated parents and cash-strapped schools.

The court is considering an appeal from the parents of an autistic teen in Colorado who say their public school did not go far enough in helping their son. They want to be reimbursed for the cost of sending him to private school.

The case could have major implications for millions of disabled students who rely on schools to make special arrangements. School districts warn that imposing higher standards will be too costly and encourage parents to make unrealistic demands.

“If we suddenly adopt a new standard, all over the country, we’ll have judges and lawyers and people interpreting it differently,” Justice Stephen Breyer said.

The debate centers on the Individuals with Disabilities Education Act, a federal law that requires a “free and appropriate public education” for disabled students. The Supreme Court last considered the issue in a 1982 case that said the law requires schools to come up with a plan that gives the student “some educational benefit.”

But lower courts have disagreed over exactly what that phrase means and how far a school must go. Some courts say it can be anything greater than a trivial effort, while others have required schools to do more.

Advocacy groups say the confusion has left wide disparities among states in the level of educational benefits that schools offer to children with special needs.

Chief Justice John Roberts told Neal Katyal, representing the Douglas County School District near Denver, that the standard seems to require more than just a minimum effort from schools.

“It says ‘some benefit,’ but you’re reading it as saying ‘some’ benefit and the other side is reading it as saying some ‘benefit,'” Roberts said, to laughter, as he switched his emphasis on the words.

In the case before the court, the boy known only as Endrew F. attended public school outside Denver from kindergarten through fourth grades, where he received specialized instruction to deal with learning and behavioral issues.

In 2010, Endrew’s parents decided to send him to private school after saying they were frustrated by his lack of progress. They want to be reimbursed for his tuition — about $70,000 a year — because they claim public school officials didn’t do enough to comply with the law.

The Colorado Department of Education denied their claim, saying the school district had satisfied its obligations under the law. The federal appeals court in Denver upheld that decision, ruling that the school district met its duty to provide more than a “de minimus” effort.

The family’s attorney, Jeffrey Fisher, argued that the law requires more than “just-above-trivial” benefits. Most of the justices seemed to agree and spent much of the session trying out different words that would convey the right message to lower courts.

Fisher urged the justices to make clear it requires benefits designed “to provide substantially equal educational opportunities.”

But Breyer and Justice Elena Kagan said they had problems with the word “equal” since the law focuses on what’s best for individual students. Fisher then suggested schools at least had to offer the kind of support that allows a disabled child to progress from grade to grade.

Justice Department lawyer Irv Gornstein, arguing in support of the parents, said the schools’ obligation should be described as making “significant progress towards grade-level standards.”

Breyer wondered about adding “significant and appropriate.” Gornstein said he had no problem with that formulation.

Justice Samuel Alito later said he was frustrated by the “blizzard of words” that could mean anything when read literally.

“What everybody seems to be looking for is the word that has just the right nuance to express this thought,” Alito said.

Katyal, the school districts’ lawyer, suggested the high court didn’t need to clarify anything because the current standard “had bite” in the lower courts.

But Kagan strongly disagreed.

“If somebody said to you, write a standard with bite, I doubt you would come up with the words “more than merely de minimis,” she said.

A ruling is expected by the end of June.