One juror said he "wondered if black people even have souls".
The US Supreme Court on Monday declined to hear the case of a black man who was sentenced to death for murder by a jury which included a white man who made racist remarks.
Keith Tharpe is on death row at a prison in the southern state of Georgia after being convicted of the 1990 kidnapping and murder of his sister-in-law, Jaquelin Freeman.
Lawyers for Tharpe have been seeking to have the sentence thrown out on the grounds that one of the jurors who heard the case had shown racial bias.
Juror Barney Gattie, who has since died, used racial slurs in an interview seven years after Tharpe's 1991 conviction and said he "wondered if black people even have souls."
The Supreme Court issued a last-minute stay of execution to Tharpe in September 2017 but it declined on Monday to hear his claim of juror bias.
The nation's highest court did not give its reasoning for refusing to hear the case.
Justice Sonia Sotomayor cited procedural questions in agreeing with the decision not to hear Tharpe's case although she said it had "uncovered truly striking evidence of juror bias."
"That evil often presents itself far more subtly than it has here," Sotomayor said, adding that eliminating racial prejudice from the administration of justice is "far from done."
Marcia Widder, a lawyer for Tharpe, condemned the decision.
"Allowing Mr. Tharpe's death sentence to stand is an affront to the fairness and decency to which we, as a society, should aspire," Widder said.