HUNTSVILLE, Texas (AP) — The U.S. Supreme Court on Wednesday stopped the execution of condemned prisoner Hank Skinner about an hour before he could have been taken to the Texas death chamber.

Skinner asked the court and Gov. Rick Perry for the delay for DNA testing that he insisted could clear him in a triple slaying.

The brief order grants him the delay but does not ensure he will get such testing. Perry had not decided on the delay.

Skinner, 47, faced lethal injection for the bludgeoning and strangling of his girlfriend, 40-year-old Twila Jean Busby, and the stabbings of her two adult sons. The slayings occurred at their home in the Texas Panhandle town of Pampa on New Year’s Eve in 1993.

The court order came as relatives of Busby were climbing the steps of the Huntsville prison to prepare to witness his punishment.

In the order, the justices said they would put off the execution until they decide whether to review his case. If the court refuses the review, the reprieve is lifted, according to the order, and that would make Skinner eligible for another execution date.

Skinner, in a small holding cell a few feet from the death chamber, expressed surprise when was informed of the reprieve in a phone call from his lawyer.

‘‘I had made up my mind I was going to die,’’ he said. ‘‘I’m eager to get the DNA testing so I can prove my innocence and get the hell out of here.

‘‘I’m greatly relieved. I feel like I really won today.’’

Rob Owen, Skinner’s lead attorney and a University of Texas law professor, said the court action suggested the justices believed ‘‘there are important issues that require closer examination.’’

‘‘We remain hopeful that the court will agree to hear Mr. Skinner’s case and ultimately allow him the chance to prove his innocence through DNA testing,’’ he said.

Skinner, splattered with the blood of at least two of the victims, was arrested about three hours after the bodies were found. Police found him in a closet at the trailer home of a woman he knew.

The former oil field and construction worker said he was present when the three were killed but couldn’t have committed the murders. Skinner said a combination of vodka and codeine left him passed out on a couch and physically incapable of clubbing Busby 14 times with an ax handle and stabbing her sons, Elwin ‘‘Scooter’’ Caler, 22, and Randy Busby, 20.

‘‘I’ve been framed ever since,’’ he said last week. ‘‘They’re fixing to kill me for something I didn’t do.’’

Prosecutors argued Skinner wasn’t entitled to testing of evidence that wasn’t analyzed before his 1995 trial. Courts over the years since his conviction have agreed, rejecting his appeals.

Skinner’s lawyers want to pursue in federal district court a civil case against the Gray County District Attorney, whose office prosecuted Skinner initially. That suit seeks to make evidence available for testing.

They’d made a similar appeal to Perry.

Skinner’s attorneys want DNA testing on vaginal swabs taken from Busby at the time of her autopsy, fingernail clippings, a knife found on the porch of Busby’s house and a second knife found in a plastic bag in the house, a towel with the second knife, a jacket next to Busby’s body and any hairs found in her hands that were not destroyed in previous testing. Only the hairs were tested previously and those results were inconclusive, according to court documents.

Skinner’s trial lawyer, Harold Comer, chose not to test all the evidence because he feared the outcome would be more damaging to his client.

Comer said he now favors the testing but defended his trial strategy.

‘‘I would make the same decision with the same circumstances again,’’ he said.

Trial prosecutor John Mann, who has since died, also did not have all the evidence tested. Current District Attorney Lynn Switzer, now the defendant in Skinner’s lawsuit, declined to comment about the case as Skinner’s execution neared. Lawyers representing her office challenged the suit as improper.

Skinner would have been the fifth person executed this year in Texas, the nation’s most active capital punishment state. Twenty-four people were put to death in Texas in 2009.