The National Alliance on Mental Illness (NAMI) said in a statement it had requested that the execution of John Ferguson, sentenced to death for the murders of eight people in the 1970s, be stopped because it violated the constitution.
Ferguson, a paranoid schizophrenic who refers to himself as the "Prince of God", is set to be executed on August 5 at 2200 GMT at Raiford prison.
NAMI said in a statement the execution would violate the constitution if it went ahead because Ferguson could not have a rational understanding of what was happening to him.
"The death penalty is not constitutionally allowable as a punishment for John Ferguson because his delusions prevent him from understanding the nature of what is happening to him," NAMI's national director of policy and legal affairs Ron Honberg said.
"The constitutional principle does not excuse his crimes, but it does point to life without parole as the appropriate sentence."
In a separate filing, the American Bar Association, representing US lawyers, had also requested that the Supreme Court review the case, citing similar concerns about Ferguson's mental health.
"Holding a person accountable is intended to be an affirmation of personal responsibility," the brief said.
"Executing someone who lacks a meaningful understanding of the nature of this awesome punishment and its retributive purpose offends the concept of personal responsibility rather than affirming it."
Ferguson, 65, has spent 35 years on death row. He was found guilty of six murders in a drug-related massacre in 1977 and was also convicted of murdering two teenagers in 1978.
His execution has been the subject of a long-running legal battle and was already suspended once in September 2012.