Washington (CNN) -- The Supreme Court granted a temporary stay of execution late Wednesday for a condemned Texas inmate who is requesting DNA testing of evidence in his case.





The order was handed down less than an hour before Henry "Hank" Skinner, 47, was scheduled to be executed by injection for the New Year's Eve 1993 killings of his live-in girlfriend and her two sons.





The Supreme Court granted the temporary stay while it considers whether to take up Skinner's broader appeal. It was not immediately clear when the court might consider the case, but there was no indication a decision would be made before Thursday.





Skinner's attorneys maintain that DNA testing of the evidence could establish his innocence and determine the real killer.





"This action suggests that the court believes there are important issues that require closer examination," defense attorney Robert Owen said of the temporary stay. "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."





Skinner heard the news while he was eating what was to be his last meal, according to Michelle Lyons, a spokeswoman for the Texas Department of Criminal Justice.





He expressed relief and surprise, saying, "I had made up my mind I was going to die" and "I feel like I really won today," according to Lyons.





Skinner said he is "eager to get the DNA testing so I can prove my innocence and get the hell out of here," according to Lyons.





Texas Gov. Rick Perry has received more than 8,000 letters from Skinner's advocates urging a stay, according to the Innocence Project and Change.org, whose members and supporters have sent the letters through their Web sites.





State Sen. Rodney Ellis and state Rep. Elliott Naishtat were among those who have called for a reprieve.





"It has come to my attention that there are numerous problems with Mr. Skinner's case that raise serious questions regarding the fairness of his trial and whether or not he is guilty," Ellis wrote in a letter to Perry on Tuesday.





Word about the case has spread as far as France, where demonstrations were planned Wednesday at the U.S. Embassy in Paris by supporters of Skinner's French wife, Sandrine Ageorges.





Since Skinner's conviction in 1995, he "has tirelessly pursued access to the untested physical evidence," according to court documents filed with the Supreme Court in February.





That evidence includes vaginal swabs and fingernail clippings from Skinner's then-girlfriend Twila Busby, hairs found in her hand and two knives found at the scene, along with a dish towel and a windbreaker jacket, according to the filing.





Skinner has never denied being in the home when Busby and her sons -- Elwin Caler, 22, and Randy Busby, 20, -- were killed. However, he maintains he was incapacitated because of the "extreme quantities of alcohol and codeine" that he had consumed earlier that evening, according to the documents.





Prosecutors maintain forensic evidence gathered at the scene and witness statements point to Skinner. A female friend of Skinner's who lived four blocks away testified at Skinner's trial that he walked to her trailer and told her that he may have kicked Twila Busby to death, although evidence did not show she had been kicked. The neighbor has since recanted parts of her testimony.





Authorities followed a blood trail from the crime scene to the female friend's trailer and found Skinner in the closet, authorities said. He was "wearing heavily blood-stained jeans and socks and bearing a gash on the palm of his right hand," according to the Texas attorney general's summary of the case.





In addition, authorities said cuts on Skinner's hand came from the knife used to stab the men. Skinner said he cut it on glass. Some DNA testing was done, which implicated Skinner, but not on the items he now wants tested.





"DNA testing showed that blood on the shirt Skinner was wearing at the time of his arrest was Twila's blood, and blood on Skinner's jeans was a mixture of
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