Davis, 42, was sentenced to death for the 1989 fatal shooting of Mark Allen MacPhail, a 27-year-old Savannah police officer and father of two, the Atlanta Journal-Constitution reported.
"I am utterly shocked and disappointed at the failure of our justice system at all levels to correct a miscarriage of justice," said Brian Kammer, one of Davis' attorneys.
The surviving relatives of the slain officer urged the parole board not to commute Davis' sentence to life in prison without parole.
"We need to go ahead and execute him," said MacPhail's widow, Joan MacPhail-Harris.
Davis' legal team argued Davis was wrongly convicted.
They said there is new evidence that indicates another person at the scene was the actual trigger man.
MacPhail was shot while helping a homeless man who was being pistol whipped.
Last week Davis' supporters presented the parole board with the names of more than 663,000 people asking that Davis be granted clemency.
Among the dignitaries who wanted Davis spared was former President Jimmy Carter, Pope Benedict XVI and former FBI Director William Sessions.
Amnesty International called the parole board's decision not to grant clemency "unconscionable."
"Allowing a man to be sent to death under an enormous cloud of doubt about his guilt is an outrageous affront to justice," the group said in a release Tuesday.