The Georgia Board of Pardons and Paroles met at 9 a.m. Monday to consider granting clemency to Davis, who claims he's innocent.
Davis is scheduled to be executed Wednesday for Mark MacPhail's murder.
This will be the fourth time in four years the state has tried to execute him, but now his legal appeals are exhausted.
The board, which can commute sentences, is Davis' last hope, his attorneys said. The board allowed Davis' execution to go forward in 2008, but three new members have since joined the board.
Davis' case has captured considerable attention because of doubts some say was raised over whether he killed MacPhail, due to conflicting eyewitness testimony. In 2008, the U.S. Supreme Court granted Davis a hearing and delayed the execution, but then decided not to hear the case.
"This is a particularly unique case," said Edward DuBose, Georgia's NAACP president, reports CBS affiliate WGCL. "We believe that Troy Davis is innocent, and we believe that if this state is prepared to execute Troy Davis, they will be executing an innocent man."
Amnesty International USA, the Campaign to End the Death Penalty, the Open Door Community and the International Socialist Organization also participated in the rally.
The officer's family believes there is no doubt that Davis killed MacPhail and prosecutors say the right man was convicted.
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