The state’s highest court has rejected a motion by the man convicted in the 2005 Bourneside killings to stay his appeal so that he could seek a new trial based on evidence he said showed he was framed.

Earlier this month, the lawyer for Calvin Carnes, who is serving four consecutive life terms for the killings of four men in a Dorchester basement, told the Supreme Judicial Court that the Suffolk district attorney’s office had for over a year withheld information that potentially cast doubt on his guilt.

On Aug. 13, prosecutors provided Carnes’s lawyer, Ellen Zucker, a February 2009 affidavit from an inmate asserting that Robert Turner, who pleaded guilty to acting as an accessory to the murders, confessed that he was the real killer. Turner was sentenced to 13 years in prison.

On Friday, the Supreme Judicial Court denied that motion for the stay on his appeal without offering an explanation or calling for a hearing. In May, Zucker appealed the 2008 conviction, arguing that the trial judge in the case wrongly dismissed the one juror who believed Carnes was not guilty of the murders. The court is still considering the appeal.

Suffolk District Attorney Daniel F. Conley’s office said the decision was a victory for prosecutors, who acted appropriately.

“There was no foundation in the facts, in the evidence, or in the law to support the defendant’s motion,’’ Conley said in a statement. “In contrast, the evidence presented against Calvin Carnes at trial was credible and overwhelming.’’

Zucker said the court’s decision does not affect that appeal, nor does it prevent her from asking the Suffolk Superior Court for a new trial based on the affidavit she received in August.

She said she filed the motion in August to alert the highest court of the affidavit.