Ledell Lee, 51, was the first to be put to death out of a group of eight men that Arkansas originally planned to execute within a span of 11 days, before the expiration of one of the drugs the state uses for the lethal injection.
Lee was administered the lethal injection at 11:44 p.m. local time (12:44 a.m. ET) and pronounced dead 12 minutes later.
The scheduled executions, comprising eight in total, marked the most by a state in such a compressed period since the US Supreme Court reinstated the death penalty in the 1970s.
"That's something we had sought from the state and federal courts and had been denied, and we're making another run at it and showing that there are new techniques that came into effect literally this year that can provide results that can bear on the case", Rosenzweig said.
"We've established that modern DNA testing methods can prove Mr. Johnson's innocence, and Arkansas law clearly established that Mr. Johnson is entitled to that testing", said Karen Thompson, a staff attorney with the Innocence Project, on Tuesday after the appeal was filed.
U.S. Supreme Court Justice Samuel Alito issued a temporary stay until 8:30 p.m. CDT as the Supreme Court considered Lee's requests for a stay, while the 8th U.S. Circuit Court of Appeals issued a separate temporary stay until 9:15 p.m. Thursday as it considered a separate appeal.
Arkansas plans to execute Lee and another inmate, Stacey Johnson, on Thursday night.
Justices also denied an attempt by makers of midazolam and potassium chloride - the two other drugs in Arkansas' execution plan - to intervene in McKesson's fight over the vecuronium bromide.
Stacey Johnson claims that advanced DNA techniques could show that he didn't kill Carol Heath, a 25-year-old mother of two, in 1993 at her southwest Arkansas apartment.
Earlier this week, McKesson said it refunded the Arkansas Department of Correction (ADC) for the drug after it agreed to return the supplies.
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Gray's decision had effectively stayed all scheduled executions.
U.S. District Judge Kristine Baker had said Saturday that Arkansas' execution protocol doesn't outline what would happen if the inmate were to remain conscious even if given a double dose. The state Supreme Court on Monday, April 17 lifted Griffen's order and prohibited the judge from considering any death penalty-related cases. In federal court, Lee said a string of incompetent lawyers failed to make the case that he is intellectually disabled and thus ineligible to be executed. A court OK'd the drug earlier Thursday.
A deputy director of the Arkansas prison system says he deliberately ordered an execution drug in a way so there wouldn't be a paper trail.
The state originally set eight executions to occur over an 11-day period in April.
But amid public opposition to the death penalty - including protests in the state capital Little Rock including actor Johnny Depp and a judge linked to one of the cases - lawyers obtained stays for three other executions.
The state filed an amended plan Monday that grants attorneys for the inmates more phone access while on prison grounds.
"I have ultimate respect for the court and I'm not going to question individual decisions but I would say there is frustration among the Legislature as to the court's continued refusal to allow an execution to go through", said Sen.
Throughout it all, Lee maintained his innocence in the bludgeoning death of Reese, but a jury convicted him in 1995, and the Arkansas Supreme Court upheld that ruling in 1997.
Lee told the BBC's Aleem Maqbool in a recent interview that he was innocent, and death row was like a "living nightmare".