"It is a violation of death penalty safeguards to impose capital punishment on individuals suffering from psychosocial disabilities," said Christof Heyns, U.N. special rapporteur on extrajudicial, summary or arbitrary executions.
"It is also contrary to the United States Supreme Court ruling Atkins vs. Virginia, which held that such executions are unconstitutional," he said.
A rapporteur is a person responsible for compiling reports and presenting them to a governing body.
The Supreme Court ruled 6-3 June 30, 2002, that executing mentally retarded individuals violates the Eighth Amendment's ban on cruel and unusual punishment.
Warren Hill was convicted of murder in Georgia and Yokamon Hearn was convicted of murder in Texas.
Their convictions have been the subject of a number of legal appeals based on the defendants' mental health.
The five-member Georgia State Board of Pardons and Paroles rejected Hill's clemency Monday, putting him on track to be executed by lethal injection Wednesday.
The Georgia Department of Corrections Tuesday said it would postpone his execution for five days as it changes its lethal-injection protocol to a single drug, pentobarbital, from a combination of three drugs.
Hill's lawyer has asked the Supreme Court to stay Hill's execution because of the Atkins vs. Virginia ruling.
The lawyer argues this standard should apply to Hill, who has an IQ of about 70.
In 1991, a jury convicted Hill of murder and sentenced him to death for killing Joseph Handspike, another inmate in the prison where Hill was serving a life sentence for the 1986 killing of his girlfriend.
Hearn, convicted in the 1998 killing of a 23-year-old stockbroker from Plano, about 20 miles north of Dallas, was scheduled to die by lethal injection Wednesday.
Texas said last week it switched to the single-drug execution and Hearn would be the first prisoner executed under the single-drug procedure.
Hearn's lawyers have appealed to the Supreme Court, arguing that Hearn suffers from a fetal brain dysfunction that should disqualify him from execution, even though his IQ is higher than what is normally associated with mental impairment.
Heyns said Tuesday an expert said Hearn probably got the dysfunction because of "his mother's alcohol abuse during pregnancy."
The U.N. official called on authorities in both states "to demonstrate the moral and legal leadership expected of the strong democracy that the United States is by commuting the death sentences of Hill and Hearn, and show the importance it gives to the fundamental right to life."
The states had no immediate comment on Heyns' appeal.