OKLAHOMA CITY — A sedative commonly used to euthanize animals may be used on death row inmates in Oklahoma to substitute one of the three drugs in the state’s lethal injection formula, a federal judge ruled yesterday.

US District Judge Stephen Friot rejected a motion by death row inmates Jeffrey David Matthews and John David Duty, who argued that the use of a drug called pentobarbital was “cruel and unusual punishment.’’

Friot said the inmates’ lawyers failed to prove that the new drug posed a “substantial risk of serious harm.’’ The judge said the two anesthesiologists who testified during yesterday’s daylong hearing agreed that a sufficient dose would render an individual unconscious and ultimately lead to death.

Earlier this year, the Oklahoma Department of Corrections ran out of sodium thiopental, a key component in the three-drug cocktail that causes unconsciousness. The department changed its protocol to allow for the use of pentobarbital, a similar drug.

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