The 61-year-old inmate, who also had been convicted of wounding a second police officer, was declared dead at 7:14 p.m. at the state prison near Starke after staff administered a fatal dose of drugs, The Miami Herald reported.
Valle, who did not make a final statement, was strapped to a gurney while receiving the lethal injection.
He consumed most of his last meal, which consisted of fried chicken breast, white rice, garlic toast, a Coca-Cola and peach cobbler, the newspaper said.
During the day, Valle was allowed to spend a few hours with members of his family, including his daughter Rebecca, a niece and a sister. He also spent time with a lay Catholic chaplain.
Corrections Department spokeswoman Gretl Plessinger described Valle as "very calm" 2 hours before his execution, which occurred after final defense appeals to stop it went unanswered by the U.S. Supreme Court.
Some relatives of Louis Pena, the officer Valle was convicted of killing, had been expected to witness the execution.
Former colleagues of Pena were at the prison.
"I am glad this day is finally here," said Harry S. Pickering, a retired police lieutenant who called Pena "a fine man and a superb officer."
Valle was put to death with a new combination of drugs, a move that was opposed by the maker of one drug. Lundbeck Inc. told Florida Gov. Rick Scott using one of its untested products in an execution "contradicts everything" the company is in business to do.
Pentobarbital -- the barbiturate Georgia used last week as part of the lethal drug-mix injection that killed convicted killer Troy Davis -- has not been proven in clinical tests to produce the desired result or effect "outside of the approved labeling," Lundbeck President Staffan Schuberg said in a letter to Scott.
He expressed his "adamant" opposition to using the sedative and anti-seizure medicine.
Some doctors and legal experts say pentobarbital could inflict extreme suffering on prisoners as they die.
"Use of our products to end lives contradicts everything we're in business to do, which is to provide therapies that improve people's lives," Schuberg's letter said.
Scott and his press office had no immediate response to a United Press International phone message and e-mail seeking a comment on the letter.
A British doctor had sought Monday to stop the execution, filing a petition with Florida's Supreme Court, but the court rejected his petition Tuesday.
A Miami-Dade Circuit judge ruled Aug. 3 pentobarbital was suitable to render a condemned inmate unconscious before two other fatal drugs were administered.
The U.S. Food and Drug Administration has not approved the drug for use in executions but has declined to enforce a ban against states using it.
Pentobarbital, marketed under the name Nembutal, is increasingly used by some of the 35 states with the death penalty as an alternative to the anesthetic sodium thiopental, better known as Sodium Pentothal, whose only U.S. producer, Hospira Inc., stopped making it in January to protest its use in capital punishment.
Lundbeck, the U.S. subsidiary of Denmark's H. Lundbeck A/S, announced July 1 it would no longer sell Nembutal to prisons in states that carry out executions.
Florida and other states already had stockpiles, allowing them to keep using it unless ordered by U.S. courts to stop.
Valle was convicted in the 1978 killing of Pena, who stopped Valle for a traffic violation in a stolen car. He has been sentenced to death and re-sentenced three times in legal wrangling that reached the U.S. Supreme Court, which overturned his death penalty in 1987.
Courts later reaffirmed his death penalty conviction.
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