Justices issued a stay Thursday night, the same evening Vernon Madison was scheduled to receive a lethal injection at a southwest Alabama prison.
They said Madison has suffered several strokes and is frequently confused.
"He does not understand why the state of Alabama is attempting to execute him", they said. The expert has not yet been convicted of any crimes as charges are pending.
The state has asked the court to let the execution proceed Thursday. If the petition for a writ of certiorari is denied, then the stay of execution will be automatically terminated.
Madison was sentenced to death for killing officer Julius Schulte in the city of Mobile. In the appeal this week, Madison's lawyers said he is not competent to be executed because he is legally blind, can not walk without assistance and is unable to recall the murder or understand his punishment.
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Although it may not be her intent, Waters runs the risk of stepping on her own party's response to the president's speech - Rep. And Ronald Reagan took advantage of television to show off special guests sitting in the crowd, a custom still in practice.
Justices noted then that federal courts' review of Madison's case is constrained because of a 1996 law meant to limit federal judges' second-guessing of state court decisions.
Attorney Bryan Stevenson said they were "thrilled" by the ruling and killing Madison would have been "unnecessary and cruel", reports the Associated Press.
"N$3 o state now allows a judge to override a jury's capital sentencing verdict".
Vernon Madison, one of Alabama's longest-serving death row inmates, appears in a booking photo provided by the Alabama Department of Corrections.
But the U.S. Supreme Court in November reversed that decision, saying court precedent had not established "that a prisoner is incompetent to be executed because of a failure to remember his commission of the crime". However, appealate courts overturned Madison's convictions twice based on prosecutorial misconduct.
Michael Schulte, the slain officer's son, said Friday that last-minute execution stays - the second Madison has received within two years - have been hard for his family and mean 'this tragedy isn't finished'. Three justices would not have granted the stay: Clarence Thomas, Samuel A. Alito Jr. and Neil Gorsuch.