The planned executions have renewed the debate over lethal injection in particular and capital punishment in general, which has been in decline for almost two decades.
The legal fight in Arkansas, which last put someone to death 12 years ago, came after the number of USA executions fell to a quarter-century low in 2016.
Bruce Ward was also scheduled to be executed Monday night and had been granted a stay by the state Supreme Court.
Arkansas Gov. Asa Hutchinson released a statement saying he was disappointed in the delay.
Two other inmates are slated for execution Thursday.
VARNER, Ark. (AP) Arkansas officials vowed to carry out a double execution later this week after the U.S. Supreme Court scuttled the state's plan to resume capital punishment for the first time in almost 12 years with a ruling issued minutes before a condemned man was scheduled to die. At the time, Justices Sonia Sotomayor and Stephen Breyer dissented.
Mckesson has said it will continue its "efforts to facilitate the return of our product and ensure that it is used in line with our supplier agreement". The court said it granted the stays due to McWilliams v. Dunn, a case pending before the U.S. Supreme Court involving the question of whether indigent defendants are entitled to independent expert witnesses.
Braden said Ward is schizophrenic and Davis has organic brain damage and is intellectually disabled.
The state also argued that U.S. District Judge Kristine Baker abused her discretion on Saturday when she ruled about potential harm from midazolam.
Attorneys for the eight were likely to appeal the federal appeals court ruling to the U.S. Supreme Court. The issue in that case is about one of the drugs scheduled to be used in the lethal injections. Arkansas officials originally scheduled eight executions from 17-27 April. They filed a separate petition for stays on Monday with the U.S. Supreme Court over a procedural matter.
Arkansas is making preparations for a series of executions that, as of late morning Monday, it is legally barred from carrying out.
A rally, at which Bishop Taylor was present, was held outside the Arkansas State Capitol April 14 calling for the executions to be stopped.
The state would use a three-drug lethal injection protocol.
State law requires a 30-day comment period on favourable recommendations, but those 30 days expire after Arkansas' midazolam supply.
Earlier in the day, the state had cleared two of the main obstacles to resuming executions.
Fresenius Kabi USA, a subsidiary of the German company Fresenius Kabi, said last week that it appeared to have manufactured the potassium chloride the state plans to use. Twice in 1997, Texas executed eight prisoners in a single month, according to the Death Penalty Information Center. But they are on a tight schedule: Executions were scheduled to begin Monday night, and if the legal proceedings take more than two weeks, the midazolam supply will have expired before any of the executions can take place.
The state has appealed both rulings and asked the higher courts to work quickly to review the decisions. Some medical experts have claimed it is not proven to be effective as an anesthetic, thus exposing an inmate to the risk of severe pain as the other drugs are administered.
Arkansas Attorney General Leslie Rutledge filed a motion to have the stay in one case vacated, and the high court rejected the request to vacate without explanation.