A former Dallas accountant condemned for fatally shooting his two young daughters was put to death Thursday night in Texas.

John Battaglia was executed for the May 2001 killings of his nine-year-old daughter, Faith, and her six-year-old sister, Liberty. Battaglia and his wife had separated, and he shot the girls at his Dallas apartment during a scheduled visit.

His lethal injection was the nation’s third this year, all in Texas. The punishment was delayed more than three hours until the US supreme court rejected appeals from his lawyers to review his case. They contended the 62-year-old was delusional and mentally incompetent for execution, and that a lower court improperly refused Battaglia’s lawyers money to hire an expert to further examine legal claims regarding his mental competency.

Battaglia smiled as the mother of his slain children, Mary Jean Pearle, and other witnesses to his execution 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 them back up and lifted his head. “Am I still alive?” he asked.

Then the powerful sedative pentobarbital began to take effect. “Oh, I feel it,” he said. He gasped twice and started to snore. Within the next few seconds, all movement stopped.

The time of death: 9.40pm central time, 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. She returned several minutes later to watch as a physician examined Battaglia and pronounced him dead. Pearle declined to be interviewed.

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 was competent.

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 Attorneys contended the state’s supply was outdated and Battaglia was at risk for unconstitutionally cruel punishment.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 master’s degree showed he had the “motive and intellectual capability to maintain a deliberate ploy or ruse to avoid his execution”.

According to prosecutors, Battaglia became enraged that Pearle had notified police about harassment, and he used a visit with their daughters to act on his anger. Pearle returned a call from one of her daughters and heard Faith pleading with her father, who put the call on speakerphone. Pearle heard her daughters crying out and gunshots on the line, and then called 911.

At the time of the killings, Battaglia was on probation for a Christmas 1999 attack on Pearle. Faith was shot three times, Liberty five. Hours later, Battaglia was arrested outside at a tattoo shop where 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.

Battaglia told the Dallas Morning News in 2014 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,” he said. “I am a little bit in the blank about what happened.”