A convicted killer who spent more than 36 years on death row in Tennessee was executed by electric chair yesterday, the second time in five weeks that the state used electrocution to carry out a death sentence.

David Miller, 61, was pronounced dead at the Riverbend Maximum Security Institution in Nashville, according to a statement by the Tennessee Department of Correction.

Asked by the warden whether he had any last words before he was executed, Miller replied: "Beats being on death row," department spokesman Tylee Tracer said.

Miller, convicted of first-degree murder for the 1981 killing of a 23-year-old woman, Lee Standifer, had been on death row since March 1982.

Edmund Zagorski, a convicted double murderer, was executed by electric chair on Nov 1, the first time Tennessee had used electrocution to carry out capital punishment since 2007.

His was the first execution by electrocution anywhere in the United States since 2013.

Earlier in the evening, the US Supreme Court rejected Miller's final appeals. Justice Sonia Sotomayor dissented from the majority ruling, as she did when the high court denied Zagorski's petition for a stay.

"Such madness should not continue. Respectfully, I dissent," Sotomayor wrote in the Miller opinion.

Tennessee governor Bill Haslam declined an 11th-hour bid for clemency, the governor's office said in a statement yesterday.

Miller chose to be executed by electrocution because he believed it would be less painful than lethal injection, according to court documents.

The US Supreme Court in October denied a legal challenge by Tennessee death row inmates to the state's mix of lethal drugs, which has led to some flawed executions in recent years.

Lethal injection is the preferred method of putting people to death in all US states that have the death penalty, according to the Death Penalty Information Centre.

The day after Zagorski's execution, Miller and three other Tennessee death row inmates filed another lawsuit in US District Court in Nashville arguing that the state's lethal injection and electrocution protocols violated the US Constitution's ban on cruel and unusual punishment. The lawsuit said a firing squad was a less painful alternative.

The Sixth US Circuit Court of Appeals ruled against the inmates on Nov 28 and said a firing squad was an outmoded method of execution.

- Reuters