Death row prisoner Richard Glossip is due to be executed later after the Governor of Oklahoma rejected an appeal.
Mary Fallin had been asked for a 60-day delay to allow Glossip's lawyers to find new evidence which could exonerate him.
Governor Fallin rejected the application, arguing that a dossier brought to her office by his legal team reveals no "credible evidence of Richard Glossip's innocence".
His case has been featured by Sky News because of the unusual nature of the conviction.
:: Why I'm A Witness At An Execution In Oklahoma
Dead Man Walking actress Susan Sarandon has said she believes he is "clearly innocent".
Glossip was convicted of the murder of his boss Barry Van Treese in 1997 because the killer, Justin Sneed, said Glossip had paid him to do it.
There was no physical evidence linking him to the crime, just the testimony of the teenager who escaped the death penalty in return for testifying against Glossip. He is serving a jail sentence, while Glossip faces death.
In a statement, Governor Fallin said: "After reviewing it with my legal team, we have determined the vast majority of the limited content they have presented is not new; furthermore, we find none of the material to be credible evidence of Richard Glossip's innocence.
"After carefully reviewing the facts of this case multiple times, I see no reason to cast doubt on the guilty verdict reached by the jury or to delay Glossip's sentence of death."
His lawyers have already filed a new claim in the Oklahoma Court of Criminal Appeals, but it relies on judges agreeing the evidence is new and significant.
On Monday they revealed they had a statement from a prison inmate who knew Justin Sneed and heard him boast about implicating Glossip.
But the Oklahoma County District Attorney David Prater dismissed the evidence as a "bull***t PR campaign".
He told Sky News: "We're working with the rule of law here. It wouldn't matter if I had a question about Mr Glossip's guilt, but I do not. And at some point this process has to stop."
On Tuesday a rally was held in the grounds of the Oklahoma State Capitol next to a monument of the Ten Commandments.
Speakers called for the state to refrain from killing Glossip.
Among those addressing the gathering was Nathson Fields, a former death row prisoner who was exonerated after a key witness recanted, and the judge in his case was convicted of accepting bribes.
He told Sky News: "We all make mistakes. The judicial system is comprised of people who are human beings and as human beings we all make mistakes."
Glossip will be not be allowed to spend his final hours with his spiritual adviser Sister Helen Prejean.
The prison changed the rules a year ago after the botched execution of Clayton Lockett , who took three quarters of a hour to die. Now only lawyers are allowed to visit prisoners in the hours up to execution.
:: Listen To Richard Glossip's Story In Ian Woods' Podcast: Another Dead Man Walking
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