AUSTIN, Tex. — An appeals court panel in New Orleans on Wednesday stayed the execution of a Texas man in a case that has gained national attention as a test for issues surrounding mental illness.

The decision, by a three-judge panel of the United States Court of Appeals for the Fifth Circuit, said that the court needed more time to consider the larger issues in the case.

The man, Scott Panetti, 56, was scheduled to die Wednesday for killing his wife’s parents with a rifle in 1992 as his horrified wife and daughter looked on. Mr. Panetti represented himself at his trial, wearing a cowboy costume with a purple bandanna while trying to call more than 200 witnesses, including the pope, John F. Kennedy and Jesus.

“It appears to us that cooler legal minds have prevailed and are preventing Texas from completing its rush to execute a severely mentally ill man,” said Kathryn Kase, Mr. Panetti’s lead lawyer and executive director of the Texas Defender Service, which represents people facing the death penalty.