Robert Glen Coe, 43, was to die by lethal injection at 1 a.m. Thursday for the 1979 kidnapping, rape and murder of 8-year-old Cary Ann Medlin.
U.S. District Court Judge Aleta Trauger blocked the execution to consider a petition by Coe's attorneys contending he is not mentally competent for execution.
Coe's attorneys say he is insane and executing him would violate the 8th Amendment's ban on cruel and unusual punishment. The state Supreme Court has found him sane for execution.
Trauger did not set a deadline for when she would rule on the petition. However, she set a Monday deadline for state and defense attorneys to file motions concerning another matter: whether Coe can have an attorney present for his execution.
That deadline indicates the execution may be delayed at least until Monday.
The Tennessee Attorney General's office filed a motion with the 6th U.S. Circuit Court of Appeals to vacate Trauger's stay, but the appeals court refused.
As all the legal wrangling went on in Nashville, the girl's family held a memorial service at her grave in Greenfield, about 100 miles north of Memphis.
They had planned to travel to Nashville to witness Coe's execution.
"I keep hearing the words 'due process' and 'I have to be fair.' I understand all that with my head, but my heart doesn't really hear it. I want it to be over,'' said Charlotte Stout, the girl's mother.
Tennessee last executed an inmate in 1960.
The case has drawn attention from death penalty opponents because Tennessee is the only state in the South which has not resumeexecutions since the death penalty was reinstated in 1976.
According to the Death Penalty Information Center, 503 of the 624 U.S. executions carried out since 1976 have been in the South, 287 of them in Texas and Virginia alone. Tennessee has 97 death row inmates, including Coe.
A state court judge ruled in February that Coe was competent on the basis of a number of mental examinations.
On Tuesday the U.S. Circuit Court of Appeals for the Sixth Circuit, based in Cincinnati, overturned a stay granted by another federal judge, and Tennessee Gov. Don Sundquist turned down a request for clemency.
Coe would be executed at the Riverbend prison near Nashville by lethal injection. He had already requested a final meal of catfish, fries, slaw, pecan pie and sweet tea.
Today, the United States is the only Western democracy in which the death penalty is still used. The punishment has been abolished by its closest neighbors and allies, who routinely denounce the practice in the United States.