Troy Davis's case has attracted international attention, and an online protest has accumulated nearly one million signatures because of doubts expressed in some quarters over whether he killed police officer Mark MacPhail in 1989.
Since his conviction, seven of nine witnesses have changed or recanted their testimony, some have said they were coerced by police to testify against Davis and some say another man committed the crime.
No physical evidence linked Davis to the crime.
Davis's best hope of avoiding execution, set for 7pm local time yesterday, lay with the Georgia Board of Pardons and Paroles but on Tuesday it denied him clemency following a one-day hearing.
"Troy is so insistent of his innocence that he is willing to take a polygraph. I think it's a bit of a risky strategy.
"Polygraph tests are not the most solid type of evidence," said Laura Moye, a spokesman for Amnesty.
"There are a number of legal filings at a number of different courts that they [his lawyers] are trying to see what they might be able to do to try and stop this execution," Moye said.
Davis was convicted of murdering MacPhail outside a Burger King restaurant, shooting him twice as he went to rescue a homeless man who was being beaten.
The victim's family says Davis is guilty and should be executed.
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