In a brief statement, the five-member board, which is appointed by the governor, said that its members “have not taken their responsibility lightly and certainly understand the emotions attached to a death penalty case.”

Mr. Davis’s supporters were reaching out to the prosecutor in the original case, asking that he persuade the original judge to rescind the death order. Benjamin Jealous, head of the National Association for the Advancement of Colored People, who planned to visit Mr. Davis on Wednesday, was trying to ask President Obama for a reprieve.

The Innocence Project, which has had a hand in the exoneration of 17 death-row inmates through the use of DNA testing, sent a letter to the Chatham County district attorney, Larry Chisolm, urging him to withdraw the execution warrant against Mr. Davis, although there is no DNA evidence at issue in the case.

Regardless of whether those hope-against-hope efforts work, the N.A.A.C.P. and others said they would call for the Department of Justice to investigate the case as a civil rights violation, asking that the original police investigation and the legal process that led to Mr. Davis’s conviction be examined.

“It harkens back to some ugly days in the history of this state,” said the Rev. Raphael Warnock of Ebenezer Baptist Church, who visited Mr. Davis on Monday.

But for the family of the slain officer, and countless others who believe that two decades worth of legal appeals and Supreme Court intervention is more than enough to ensure justice, it is not an issue of race but of law.