The US state of Georgia has executed a 72-year-old man, its oldest death row inmate, for the killing of a store manager during a robbery decades ago.

Brandon Astor Jones was pronounced dead in the early hours of Wednesday morning after an injection of barbiturate pentobarbital at the state prison in Jackson. He was convicted in the 1979 shooting death of suburban Atlanta store manager Roger Tackett.

Jones declined to make a final statement in front of witnesses but agreed to have a prayer read.

Jones was initially still with his eyes closed and then swallowed a couple of times and moved his head slightly. He opened his eyes and turned his head to his left, appearing to look at a clock on the wall. Then he closed his eyes again and took a few deep breaths before falling still.

The execution was delayed while the US Supreme Court considered appeals from Jones's lawyers. They asked the justices to block the execution for either of two reasons: because Jones was challenging Georgia's lethal injection secrecy law or because he said his death sentence was disproportionate to his crime.

The court denied the requests for a stay.

The challenge to Georgia's strict execution secrecy law sharply divided the 11th US Circuit Court of Appeals. The law classifies the identifying information of any person or entity who participates in an execution as a "confidential state secret".

Jones's lawyers argued the state's execution method carries "a substantial risk of significant harm", violating his constitutional right against cruel and unusual punishment. But because of the secrecy law, they argued, they do not have enough information to make that claim, which violates his constitutional right to due process.

Three-judge panels of the 11th Circuit had already rejected similar arguments, setting a binding precedent. But because of divided opinions expressed by judges on those panels, Jones's lawyers asked the full 11-judge court to consider their arguments. The court voted 6-5 to deny that review, but several judges offered strongly worded dissenting opinions.

"Today Brandon Jones will be executed, possibly in violation of the constitution. He may also be cruelly and unusually punished in the process. But if he is, we will not know until it's too late - if ever," wrote Circuit Judge Robin S Rosenbaum, adding that she believes the secrecy law denies Georgia death row inmates of their due process rights and may deprive them of their right to access to the courts.

According to evidence at his trial, Jones and another man, Van Roosevelt Solomon, were arrested at a Cobb County store by a policeman who had driven a stranded motorist there to use a pay phone on June 17, 1979. The officer knew the store usually closed at midnight and was suspicious when he saw a car with the driver's door open and lights still on in the store.

The officer saw Jones inside the store, prosecutors have said. He entered and drew his weapon after hearing four shots. He found Jones and Solomon just inside a storeroom door and took them into custody. Tackett's body was found inside the storeroom.

Tests showed each man had recently fired a gun or handled a recently fired gun, prosecutors said. The cash drawer had been removed and was found wrapped in a plastic bag.

Jones was convicted in October 1979 and sentenced to death. A federal judge in 1989 ordered a new sentencing hearing because jurors had improperly been allowed to bring a Bible into the deliberation room. He was resentenced to death in 1997.

Solomon, who was also convicted and sentenced to death, was executed by electric chair in February 1985.