Hill has received support from various activists and from former President Jimmy Carter and his wife Rosalynn.
"Georgia should not violate its own prohibition against executing individuals with serious diminished capacity," President Carter said in a statement.
Hill was originally set to be executed in July, but the state delayed his execution when it changed its execution procedure from a three-drug combination to a one-drug method. The state Supreme Court then further delayed the execution after Hill's lawyers filed a challenge saying corrections officials violated administrative procedure when they made the change. The state's high court earlier this month denied that challenge, and Hill's execution was reset for Tuesday.
Georgia's supply of the single drug it uses to perform executions is scheduled to expire next month, and state officials haven't said whether they've found a way to get more of the powerful sedative pentobarbital. Another inmate, Andrew Allen Cook, is set to be put to death Thursday, but no other executions are currently scheduled.
Hill's lawyers argue that he is mentally disabled and therefore shouldn't be executed. The state maintains that the defense failed to meet its burden of proving beyond a reasonable doubt that Hill is mentally disabled.
Death penalty defendants in Georgia have to prove they are mentally disabled beyond a reasonable doubt to avoid execution, the strictest standard in the country. Hill's lawyers have said the high standard for proving mental disability is problematic because psychiatric diagnoses are subject to a degree of uncertainty that is virtually impossible to overcome. But Georgia's strict standard has repeatedly been upheld by state and federal courts.
Georgia passed a law in 1988 prohibiting the execution of mentally disabled death row inmates, and the U.S.Supreme Court ruled in 2002 that the execution of mentally disabled offenders is unconstitutional.