Cameron County District Attorney Luis V. Saenz said his office is working to schedule a new execution date for the Brownsville father convicted of beheading his children.

“It's important for us and the community because this is something that no one will ever forget,” Saenz said. “But as long as he's alive, as long as he's breathing, as long as taxpayers are paying for his life, it is an open wound."

John Allen Rubio, 45, was originally sentenced to death in 2003 after being found guilty of killing his 2-month-old daughter Mary Jane Rubio, and his two stepchildren, Julissa Quesada, 3, and 1-year-old John E. Rubio.

A new trial was ordered shortly afterward, but a jury convicted him again in 2010 and sentenced him to death. Rubio filed multiple appeals since then.

On Monday, the U.S. Supreme Court denied Rubio’s request to hear his case.

According to Saenz, Rubio is still legally able to file motions to stop the execution.

“I won't be surprised if he tries to again escape accountability by filing something frivolous, but we'll be ready to fight him on that,” Saenz said. “We'll continue fighting until we bring justice for the three babies that lost their lives.”

Channel 5 News reached out to Rubio’s defense team for comment. They did not respond as of Tuesday evening.