Texas' top criminal court has stayed the execution of a death row inmate whose attorneys argue he didn't kill a 19-year-old woman nearly two decades ago.

The Texas Court of Criminal Appeals issued a stay Monday that halts the March 5 execution of Rodney Reed. Reed was convicted of the 1996 rape and strangling death of Stacey Stites, a grocery store worker whose body was found off the side of a road in Central Texas.

The clock has been ticking down the short time left before Rodney Reed's execution. His family, who are from Bastrop, say the past few days leading up to this moment were agonizing. Reed's brother Roderick says the news of the stay is hard to describe.

"It's a feeling that I really can't put into words because it was tremendous. It was, for us, it's a victory," he said. "This has been like a nightmare for our family."

Reed's attorneys argue that another man, police officer Jimmy Fennell, killed Stites and that forensic evidence suggests she was killed hours before the time jurors were told at Reed's trial. Fennell was engaged to Stites when she was murdered.

Stites' sisters, however, said they've always thought Reed was guilty.

"The family has never believed that he was not guilty," Debra Oliver, Stacey Stites’ sister, said late last year.

Reed's brother says the recent rallies held in Bastrop and Austin have been crucial in calling attention to the case.

"Without people supporting us, backing us, getting out there raising their voice, screaming to the top of their lungs, we may never have got this attention,” Roderick Reed said. “They may have never even looked into it like they're doing."

No word on how long the stay of execution will last. Roderick plans on seeing Rodney on Tuesday, and he's thrilled knowing it will be a visit of celebration instead of grief.

"Tomorrow's meeting is going to be like 18 Christmases in the morning, it's just going be that big,” Roderick Reed said. “Really, really it is."

Fennell, Stites' fiance, is in jail serving an unrelated 10-year sentence for raping a woman who was in his custody.

This is the second stay of execution for Reed. The first came in November. 

Texas Attorney General Ken Paxton's office was reviewing Monday's court's ruling and did not immediately comment.

The Associated Press contributed to this report.