Image copyright Reuters Image caption John Battaglia killed the girls in his Texas apartment

"Well hi, Mary Jean," a Texas death row inmate said to his ex-wife as he was executed for murdering their two daughters in 2001.

"See ya'll later. Go ahead please," said John Battaglia, 62, as he prepared for Thursday night's lethal injection.

The former accountant murdered his six- and nine-year-old daughters in his apartment as ex-wife Mary Jean Pearl listened helplessly on the phone.

Lawyers filed a last-minute appeal to spare his life, but it was rejected.

Battaglia's legal team had asked the US Supreme Court to review his case because his "perception of reality may be so distorted that he is incompetent to be executed".

Image copyright Dallas Police Department Image caption John Battaglia with Liberty (L) and Faith

After the lethal injection was administered, he closed his eyes for several moments, opened them, smiled and asked: "Am I still alive?"

Battaglia then grinned and sighed, according to Dallas Morning News.

"Oh, here, I feel it," he said before gasping for breath and beginning to snore.

After 22 minutes Battaglia was pronounced dead at 21:40 local time (03:45 GMT on Friday).

"I've seen enough of him," his ex-wife said as she walked away from the glass window that separated her from Battaglia, according to the Associated Press.

He was the third prisoner put to death in the US this year. All the executions in 2018 have taken place in the state of Texas.

Battaglia and Ms Pearl divorced a year before the killings.

She was seeking his arrest for violating a protective order against her on the day he murdered their daughters Liberty, six, and Faith, nine.

On that evening in May 2001, Battaglia was scheduled to have dinner with the two girls when police informed him that he was violating probation and needed to surrender, court documents show.

Image copyright Handout Image caption Battaglia's ex-wife heard gunshots and screams

When the girls arrived at his Dallas apartment he called his wife and put her on speaker phone.

Faith asked: "Mommy, why do you want Daddy to go to jail?"

A few seconds later Ms Pearl said she heard her daughter say: "No, Daddy, please don't, don't do it."

Ms Pearl then heard gunshots and screams.

The girls were found dead in Battaglia's apartment after being shot multiple times, police said.

According to court documents, he went to a bar with his girlfriend after killing his daughters.

Battaglia was later arrested at a tattoo parlour where he was getting tattoos of roses to remember them.

A jury took 20 minutes to convict him in 2002.

Experts determined that he had "delusional disorder of the persecutory type" after examining him.

However, prosecutors said that Battaglia was aware of his crimes and therefore fit to be executed.