Accountant John David Battaglia who killed his daughters is executed

John Battaglia was at a nearby tattoo shop getting two large red roses inked on his left arm to commemorate his daughters when he was arrested for their murders. Photo / Supplied

A Texas accountant who murdered his two young daughters while their mother listened helplessly on the phone has been executed.

John David Battaglia, 62, received the lethal injection on Thursday night in Dallas for the 2001 killings of his 9-year-old daughter, Faith, and her 6-year-old sister, Liberty.

The punishment was carried out after the US Supreme Court rejected appeals from his lawyers to review his case, contending he was delusional and mentally incompetent for execution.

Battaglia who is scheduled for execution Thursday, Feb. 1, 2018, in Huntsville, Texas (US time). Photo / AP

Battaglia smiled as the mother of his slain children, Mary Jean Pearle, and other witnesses to his lethal injection walked into the death chamber viewing area.

Asked by the warden if he had a final statement, the inmate replied: 'No,' then changed his mind.

"Well, hi, Mary Jean," he said, looking and smiling at his ex-wife. "I'll see y'all later. Bye."

After that, he told the warden: "Go ahead, please."

Battaglia then closed his eyes and looked directly up. A few seconds later he opened his eyes and lifted his head. "Am I still alive?" he asked.

When the powerful sedative pentobarbital began to take effect, he said: "Oh, I feel it." He gasped twice and started to snore. Within a few more seconds, all movement stopped.

The time of death was 9.40pm - 22 minutes after the lethal dose began.

Pearle turned away from an execution-viewing window after Battaglia stopped breathing and walked to the back of the witness area.

"I've seen enough of him," she said before returning minutes later to watch as a physician examined Battaglia and pronounced him dead.

Battaglia, who had separated from his wife, had picked up his daughters in a shopping center parking lot for his court ordered visit with the girls.

Prosecutors said Battaglia became enraged that Pearle had notified police that he was harassing her and he used the visit with their daughters to act on his anger.

Pearle, who had gone to dinner, returned a call from one of her daughters and heard Faith pleading with her father, who had put the call on speakerphone.

"No, daddy, please don't, don't do it!" Faith begged.

Mary Jane Pearle is pictured during Battaglia's murder trial in 2002. Photo / via ABC

Pearle yelled into the phone for the children to run, then heard gunshots.

"Merry ... Christmas," Battaglia told Pearle, the words of the holiday greeting derisively divided by an obscenity.

After hearing more gunshots, Pearle called 911. At the time of the shootings, Battaglia was on probation for a Christmas 1999 attack on Pearle. His profanity-laced Christmas greeting to Pearle was an apparent reference to that.

Faith was shot three times and Liberty five. Hours later, Battaglia was arrested outside at a tattoo shop where he had two large red roses inked on his left arm to commemorate his daughters. It took four officers to subdue him.

A fully loaded revolver was found in his truck and more than a dozen firearms were recovered from his apartment.

Faith, right, was shot three times and Liberty five. Photo / Supplied

Battaglia, who has been on death row since 2002, told The Dallas Morning News in 2014 that his daughters were his 'best little friends' and that he had photos of them displayed in his prison cell.

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

His was the nation's third execution this year, all in Texas.

The 5th US Circuit Court of Appeals earlier in the day rejected an appeal that argued a lower court improperly refused his lawyers money to hire an expert to further examine legal claims of his mental competency.

Faith, 9, (right) and her 6-year-old sister, Liberty were killed at Battaglia's Dallas apartment during a scheduled visit. Photo / Supplied

The Supreme Court has ruled that prisoners can be executed if they're aware the death penalty is to be carried out and have a rational understanding of why they're facing that punishment.

Attorneys for Battaglia contended he didn't have that understanding and that the state's highest court, the Texas Court of Criminal Appeals, misapplied the Supreme Court's guidance when it ruled that Battaglia is competent.

State attorneys said the Texas courts ensured proper legal standards were followed and that Battaglia had been provided expert help and a court hearing in accordance with Supreme Court precedents.

Another unsuccessful appeal challenged the effectiveness of the pentobarbital Texas uses as its execution drug. Attorneys contended the state's supply was outdated and Battaglia was at risk for unconstitutionally cruel punishment.

A state judge and the state appeals court described Battaglia as highly intelligent, competent, not mentally ill and faking mental illness to avoid execution.

Testimony at a hearing showed Battaglia used the prison library to research capital case rulings on mental competence and discussed with his father during a phone call from jail the "chess game" of avoiding execution.

State Judge Robert Burns, who found him competent, said Battaglia's intelligence and education - he has a master's degree - shows he's not a "typical inmate" and has the "motive and intellectual capability to maintain a deliberate ploy or ruse to avoid his execution."

- AP