He was scheduled to be executed at 7 p.m. at the Georgia Diagnostic and Classification Prison in Jackson, Ga.
Davis's attorney said they are waiting for a response from the U.S. Supreme Court about a last-minute appeal that was made just hours before the execution was scheduled to take place. There was no timeframe on when the appeal would be heard by the U.S. Supreme Court.
Davis was found guilty in 1991 for killing Savannah police officer Mark MacPhail in 1989.
The Georgia Board of Pardons and Parole on Wednesday denied the request to reconsider its decision to deny Troy Davis clemency. Davis was denied clemency on Tuesday.
Two requests were made by Davis's attorneys on Wednesday morning.
A request was made to Georgia prison officials to allow Davis to take a polygraph test to prove his innocence, but prison officials denied him the test.
Another defense attorney also filed a last-minute appeal on Wednesday morning in Butts County Superior Court, claiming the ballistic testing that linked Davis to the shooting was flawed.