(CNN) -- Twice-convicted killer Warren Lee Hill was granted final-hour stays of execution on Tuesday, his attorney said.
The stays came from the 11th U.S. Circuit Court of Appeals and the Georgia Court of Appeals.
"I think we were within about a half hour of the execution," said Brian Kammer, an attorney for Hill, whose supporters say is mentally disabled.
The Georgia Court of Appeals acted on a appeal of a challenge to the way the prison handles the lethal injection drugs used in executions, while the federal appeals court issued a stay "ordering a further briefing on the issue of mental retardation," Kammer said.
Earlier Tuesday, the U.S. Supreme Court denied a stay of execution, as did the state Supreme Court, while the Georgia State Board of Pardons and Paroles similarly denied a request for clemency.
The execution had been scheduled for 7 p.m. ET at a state prison in Jackson, about 45 miles south of Atlanta.
Hill was sentenced to death for the 1990 killing of Joseph Handspike, another inmate in a Georgia state prison.
He was convicted of beating Handspike to death with a nail-studded board while serving a life sentence in the 1985 killing of his girlfriend, Myra Wright.
His lawyers have argued that Hill's IQ of 70 means he should be spared under a 2002 decision that barred the execution of the mentally disabled. But a string of state courts has said Hill doesn't qualify under Georgia law, which requires inmates to prove mental impairment "beyond a reasonable doubt."
"This is the strictest standard in any jurisdiction in the nation. Even Warren Hill, a man with an IQ of 70 who is diagnosed as mentally retarded by every doctor who has examined him, found it impossible to meet this standard of proof," Kammer said.
Handspike's family has called for the execution to be called off. The Georgia Council on Developmental Disabilities also weighed in against the execution, stating, "No other state risks the lives of those with developmental disabilities to this extreme."
Three doctors who examined Hill for the state "have now revised their opinions and find that Mr. Hill does meet the criteria for mental retardation," his lawyers argued in court papers.
But lawyers for the state have said that Hill served in the Navy, held a job and managed his money before Wright's killing -- signs that he didn't necessarily meet the legal standard for retardation, even though he has a low IQ.
Hill had previously been scheduled for execution in July, but the state Supreme Court halted the execution on procedural grounds.
Georgia has executed 52 men since the U.S. Supreme Court reinstated the death penalty in 1973, according to the Georgia Department of Corrections. There are currently 94 men and one woman under death sentence in the state.