AUSTIN, Texas (REUTERS) - Texas plans on Wednesday (March 30) to execute a man who killed his two daughters at his Dallas apartment while the girls' mother listened on the phone, hearing the gunshots and her children's screams.

John Battaglia, 60, a former accountant, is set to be put to death by lethal injection at the state's death chamber in Huntsville at 6 pm local time. If the execution goes ahead, it would the 537th in Texas since the US Supreme Court reinstated the death penalty in 1976, the most of any state.

Lawyers for Battaglia launched a last-minute appeal saying he should be spared because he suffers from severe bipolar disorder, which was not properly considered in sentencing. "Mr Battaglia has presented evidence that makes a colorable showing that his delusions make him not understand the reasoning behind his execution," they said in a filing to the U.S. Supreme Court.

Battaglia had a history of beating women and had been divorced from his wife, Mary Jean Pearl, for about a year at the time he fatally shot their two daughters, Mary Faith, 9 years old, and Liberty, 6, in May 2001, prosecutors said.

At the time of the shooting, Pearl was seeking to have him arrested for violating a protective order by threatening her.

When he had the children, he knew a warrant had been issued for his arrest, with an officer asking him to turn himself in peacefully so police did not have to take him into custody while he was with his daughters, court documents showed.

He left a message on his wife's phone. When she called back, he put the phone on speaker and demanded that his wife speak with daughter Mary Faith.

The daughter then asked: "Mommy, why do you want Daddy to go to jail?" and could be heard a few seconds later saying: "No, Daddy, please don't, don't do it." Then the mother heard gunshots and screams. Battaglia shouted an obscenity at her on the phone, the documents showed.

Pearl then hysterically called 911 and police found the dead girls in Battaglia's apartment. Both had been shot multiple times.

After the shooting, Battaglia went to a bar with his girlfriend and was arrested shortly afterward at a tattoo parlor where he was getting rose tattoos to remember his daughters, the documents showed.

It took a jury about 20 minutes to convict him.