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DALLAS (CBSDFW.COM/AP) — A new execution date has been set for a former Dallas accountant convicted of fatally shooting his two young daughters more than 15 years ago. John David Battaglia, who killed his daughters while their mother, his ex-wife, listened helplessly over the phone, is now scheduled to die in December.

State District Judge Robert Burns’ Monday order for a December 7 execution date came five months after a federal appeals court halted Battaglia’s scheduled lethal injection so an attorney could be appointed to investigate claims Battaglia may be mentally incompetent for execution.

The reprieve from the 5th U.S. Circuit Court of Appeals was issued March 30, about seven hours before Battaglia could have been taken to the Texas death chamber in Huntsville. The court said Battaglia presented some evidence of mental illness and delusions, but it was not clear if he was incompetent.

The U.S. Supreme Court has ruled that a prisoner can be executed if he’s aware that the death penalty is set to be carried out and understands why he’s facing the ultimate sentence. A hearing for Battaglia on that issue hasn’t been set yet.

Michael Mowla, an attorney appointed to represent Battaglia, didn’t immediately return a phone message left Tuesday by The Associated Press.

Battaglia, 61, was convicted of killing his daughters, 9-year-old Faith and 6-year-old Liberty, at his Dallas apartment in May 2001. He had met his ex-wife in the parking lot of a Park Cities shopping center to receive daughters for his scheduled visit.

Not long after the children were given to Battaglia, he got his former wife Mary Jean Pearle on the phone. “Why do you want daddy to go to jail,” one of the girls reportedly said to Pearle over the phone. Seconds later, Pearle heard one the children say “No, no, daddy,” then gunshots.

Authorities said the slayings were revenge for their mother’s complaints to Battaglia’s parole officer that led to a warrant for his arrest.

Battaglia is among at least seven Texas inmates scheduled for execution in the coming months.

(©2016 CBS Local Media, a division of CBS Radio Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)