HOUSTON — A federal court rejected a lawsuit by five Texas death row inmates who said the lethal drugs intended for their executions should be retested before their punishments are carried out to ensure they suffer no unusual pain.

Lawyers for the five prisoners argued to the Fifth US Circuit Court of Appeals that an agreement between the Texas Department of Criminal Justice and two other inmates to test the pentobarbital for their lethal injections should be extended to them. Failure to do so would violate their constitutional right to equal protection under the law, they said.

The appeals court on Monday agreed with a Houston federal judge’s dismissal of the lawsuit filed a month ago, calling it a ‘‘novel and flawed invocation of equal protection doctrine.’’

Texas has put 537 prisoners to death since 1982, more than any other state. It replaced its previous three-drug combination for executions in 2012 with a single dose of pentobarbital and the last 32 lethal injections have used pentobarbital from a compounding pharmacy. Attorneys for the five inmates argued that the compounded drug created significant risk of unnecessary pain prohibited by the Eighth Amendment and needed to be retested as the punishments neared.

‘‘The reality is that pentobarbital, when used as the sole drug in a single-drug protocol, has realized no such risk,’’ the appeals court panel said in its 12-page ruling.

The five inmates — Jeffery Wood, Rolando Ruiz, Robert Jennings, Terry Edwards, and Ramiro Gonzales — all had execution dates scheduled when their lawsuit against top Texas prison agency administrators was filed Aug. 12.

Since then, Wood, Ruiz, and Jennings have received reprieves unrelated to the drug lawsuit. Edwards remains set to die Oct. 19 and Gonzales on Nov. 2.

Michael Biles, the lead attorney for the inmates, said he was considering an appeal to the Supreme Court.

Associated Press