Davis, of Savannah, was convicted in 1991 for the slaying of Savannah police officer Mark MacPhail. Supporters say he deserves a new trial after several key trial witnesses recanted their testimony.
Davis' lawyers appealed to the Supreme Court after the U.S. 11th Circuit Court of Appeals in Atlanta denied his request for a new trial in April. The Supreme Court won't reconvene until September.
Davis' case has become a rallying point for death penalty opponents worldwide. His supporters include former President Carter, Nobel Peace Prize winner Desmond Tutu and Pope Benedict XVI.