John David Battaglia murdered his nine-year-old daughter, Faith, and her six-year-old sister, Liberty, in his Dallas apartment - Representational image Flickr via Creative Commons/Pi

A 62-year-old Dallas man, who had shot his two daughters to death in 2001, was executed in Texas on Thursday, 1 February.

On the night when John David Battaglia murdered his nine-year-old daughter, Faith, and her six-year-old sister, Liberty, in his apartment, he had called the girls' mother on her phone, who heard her children screaming, "No, daddy, please don't, don't do it!"

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Battaglia, who has been on death row since 2002, received the lethal injection on Thursday night after the US Supreme Court rejected appeals from his lawyers to review his case. According to Battaglia's lawyers, he was delusional and mentally incompetent for execution, the Daily Mail reported.

Mary Jean Pearle, the children's mother, and other witnesses were present at the death chamber viewing area where Battaglia's execution took place.

When the warden asked him if he had any final statement, he replied, "No." However, Battaglia immediately changed his mind and said, "Well, hi, Mary Jean, I'll see y'all later. Bye."

He then told the warden, "Go ahead, please." The time of death was 9.40pm (3.40am GMT).

According to reports, on the day of the incident, Battaglia – who was separated from his wife – had picked up his daughters from the parking lot of a shopping centre for his scheduled court-ordered visit with the girls.

The prosecutors said that Battaglia later became enraged after his wife had told the police that he was harassing her.

When Pearle, who had gone out for dinner, got a call from one of her daughters, she heard Faith pleading with her father, who had by then put the call on speakerphone.

After hearing her children screaming, she told them to run but then heard gunshots, according to the Daily Mail. It was later found that Faith had been shot thrice and Liberty five times by Battaglia in his apartment.

"Merry... Christmas," he told his wife on the phone at the time.

Police later arrested him outside a tattoo parlour where he had got two large red roses inked on his left arm to commemorate his daughters.

"I don't feel like I killed them. I am a little bit in the blank about what happened," he had said then.