A Texas man who was already being hunted for a neighbour's murder when he killed a Dallas police officer outside a club has been executed.

Licho Escamilla was put to death for the November 2001 killing of Christopher Kevin James, who was trying to break up a brawl involving Escamilla.

The 33-year-old prisoner was pronounced dead 18 minutes after the lethal injection began.

He was the 24th convicted killer executed this year in the United States, with 12 in Texas.

Before dying, Escamilla looked at the officer's daughter, who was seated a few feet away watching through a window, and told her: "God bless your heart."

He turned to his relatives watching through another window and said he loved them and everyone who supported him.

"Pope Francis, God's children has asked the state of Texas to switch my death sentence to life in prison," he said. "But the state of Texas has refused to listen to God's children.

"They will have to take that up with God."

He took two breaths as the sedative took effect, then became still. His sister cried and screamed for God not to take him.

The rumbling of motorcycles could be heard outside the prison where bikers supporting the punishment had gathered.

The US Supreme Court refused to review his case last week and no additional appeals were filed as his execution neared. The Texas Board of Pardons and Paroles on Monday decided against a reprieve and clemency.

Mr James and three other uniformed officers were off-duty but working security when the brawl started. Escamilla pulled out a gun and opened fire on the officers as they tried to end the fight.

The bullets from his 9mm semi-automatic handgun struck Mr James twice, knocking him to the ground. Escamilla then calmly walked up to the officer and fired three more shots into the back of his head before running and exchanging shots with other officers, witnesses said. A second officer was injured in the shootout.

A wounded Escamilla was arrested as he tried to carjack a truck.

About half a dozen Dallas police officers stood at attention and saluted as relatives of the officer entered the prison in Huntsville ahead of the execution.

"It's taken longer than we would have liked," said Frederick Frazier, first vice president of the Dallas Police Association.

He said he and others showed up to support Mr James and make sure he is remembered for the work he did. While officers know they are risking their lives every day, Mr James's death has been difficult for them because of how it happened, Mr Frazier added.

Mr James, 34, had earned dozens of commendations during nearly seven years on the Dallas police force after graduating at the top of his cadet class. He was working the off-duty security job to earn extra money so he and his new wife could buy a house.

Escamilla was 19 at the time of the killing and a warrant had been issued for him in the shooting death of a West Dallas neighbour nearly three weeks earlier.

Escamilla's lawyers told jurors he was responsible for Mr James's killing but argued it did not merit a death sentence because the officer was not officially on duty, meaning the crime did not qualify as a capital murder.

He was sentenced to death in October 2002. At his trial in Dallas, Escamilla grabbed a water pitcher off the defence table and threw it at the jury as the judge was reading his sentence.

Escamilla also started kicking and hitting people and hid under the table until he was subdued by deputies who triggered an electronic stun belt he was wearing.

Evidence showed Escamilla bragged to emergency medical technicians who were treating his wounds that he had killed an officer and injured another and that he would be out of jail in 48 hours. He also admitted the killing during a television interview from jail.