WASHINGTON — The Supreme Court on Tuesday appeared skeptical of the way Texas decides who must be spared the death penalty on account of intellectual disability, with several justices indicating that the state’s standards were either too strict or too arbitrary.

But there was also disagreement and confusion over precisely what the state’s standards required. A lawyer for Bobby J. Moore, a death row inmate challenging his death sentence, said the state used outdated medical standards and looked to factors rooted in stereotypes.

Scott A. Keller, the Texas solicitor general, said judges there followed the requirements of a 2002 Supreme Court decision, Atkins v. Virginia. That ruling barred the execution of the intellectually disabled but largely left it to individual states to fashion their own standards in deciding who qualifies.

It was not Texas’ goal, Mr. Keller said, “to screen out individuals and deny them relief.”

Justice Anthony M. Kennedy, who often votes with the court’s four-member liberal wing to limit the death penalty, was skeptical. “But isn’t that the effect?” he asked.