AUSTIN, Texas (AP) — A Texas appeals court on Tuesday halted the execution of a man who has spent more than 30 years on death row and had been set to die by lethal injection this week over the killings of six girls and young women found buried in the desert near El Paso.

It was the second scheduled execution in the U.S. halted on Tuesday after a federal judge stopped Louisiana’s first death row execution using nitrogen gas, which was to take place next week.

In Texas, the order was another reprieve for David Leonard Wood, who in 2009 was about 24 hours away from execution when it was halted over claims he is intellectually disabled and thus ineligible for execution.

Those claims were later rejected by a judge and Wood, 67, had been set to die Thursday. But the Texas Court of Criminal Appeals, the state’s highest criminal court, issued a stay of execution after his latest appeal, which renewed his claims of innocence.

The court put Wood’s execution on pause “until further order.” It did not elaborate on the decision in a brief three-page order.

Had Wood been executed this week, he would have spent 32 years and two months on Texas’ death row, the longest time a Texas inmate has waited before being put to death.

The 1987 murders remained unsolved for several years until authorities say Wood bragged to a cellmate that he was the so-called “Desert Killer.” The victims’ bodies were found buried in shallow graves in the same desert area northeast of El Paso.

Authorities said Wood gave rides to the victims and then drove them into the desert, where he sexually assaulted and killed them. The victims were Rosa Casio and Ivy Williams, both 23; Karen Baker, 21; Angelica Frausto, 17; Desiree Wheatley, 15; and Dawn Smith, 14.

Two other girls and a young woman were also reported missing but were never found.

Wood, a repeat convicted sex offender who had worked as a mechanic, has long maintained his innocence.

“I did not do it. I am innocent of this case. I’ll fight it,” Wood said in recent documents filed in his appeals.

On March 4, the Texas Board of Pardons and Paroles declined a request to commute his death sentence to a lesser penalty or grant him a 90-day reprieve.

His lawyers have for years sought to have hundreds of pieces of evidence tested for DNA after testing in 2011 of bloodstains on the clothing Smith wore found a male DNA profile that was not Wood. The Texas Attorney General’s Office has fought against new DNA tests and various courts have denied Wood’s request for it.

Prior to the court’s decision Tuesday, Gregory Wiercioch, one of Wood’s attorneys, said that when authorities identified Wood as a suspect, they focused on him and not on the evidence they had.

“We’ve tried to make it clear to the courts that he’s innocent, and we’ll see if anyone listens,” Wiercioch said.