Lawyers are racing against the clock to save the life of a "mentally retarded" man in Georgia who is scheduled to be put to death on Tuesday despite a US supreme court ban on executing prisoners with learning disabilities.

The execution of Warren Hill at 7pm local time on 19 February would be the first completed death sentence in Georgia since that of Troy Davis. The 2011 judicial killing of Davis, in the wake of substantial evidence of his probable innocence, prompted an outpouring of disgust across America and the world.

Hill's impending death by lethal injection has so far failed to ignite the mass outrage that marked the Troy Davis killing, but close followers of the case protest that it would be equally disturbing and unconstitutional. Writing in the Guardian, the UN special rapporteur on extrajudicial, summary or arbitrary executions, Christof Heyns, has said that "the world community is again watching Georgia with great concern as it prepares to carry out another grotesque and unjust execution."

Hill, 53, was sentenced to death for killing a fellow prisoner, Joseph Handspike, in 1990 while he was already serving a life sentence for murdering his girlfriend, Myra Wright. The Handspike family has stated publicly that they oppose his execution.

All medical specialists who have examined Hill now agree that he is "mentally retarded" – the designation of intellectual disability still widely used in the US – and should be protected under the supreme court ban. In an important break in the case, three forensic psychiatrists who had previously testified that Hill did not meet the legal criteria for "mental retardation", and was thus eligible for execution, have in recent days announced that they now believe their opinion was wrong.

All three doctors say that their original evaluation – given 12 years ago at a crucial stage in the case – was rushed and ill-conceived.

Thomas Sachy, a neuropsychiatrist, has stated in an affidavit that he came to his opinion that Hill was fit to be executed in November 2000 after having seen him only for an hour. It was the medic's first experience of a capital case, he had no experience evaluating patients with learning difficulties and almost no experience testifying in a forensic setting.

"The whole process, including my evaluation of Mr Hill, was rushed … my previous conclusions about Mr Hill's mental health status were unreliable because of my lack of experience at the time," he wrote.

In his revised opinion, reached with the benefit of 12 years of additional experience and advances in scientific knowledge and in agreement with the two other psychiatrists, Sachy now concludes that Hill does meet the criteria for mild mental retardation.

The change of testimony could prove crucial in a case that is fast hurtling towards its grim conclusion. Georgia is the only state in the union that requires death row inmates to prove beyond a reasonable doubt that they are "mentally retarded" if they wish to avail themselves of the supreme court protection and avoid execution.

Experts in the field of learning disabilities say that proving such a standard is almost impossible, especially in cases like Hill's of mild "mental retardation". All other 49 states apply a lesser definition of "mental retardation" by the "preponderance of the evidence" – in other words inmates only have to show that they are likely to be intellectually disabled to avoid the death chamber.

Brian Kammer, a Georgia lawyer who has fought to keep Hill alive for the past 16 years, said the revised testimony of the doctors was an incredibly important development. "There is now no daylight between any of the experts who have evaluated Mr Hill – in an innocence context this would now be a clear case for exoneration," he said.

Kammer has filed two emergency petitions to attempt to stay Hill's execution on Tuesday. The first is with the Georgia courts that draws on the doctors' revised testimony to argue that the execution should be put on hold, supplemented by a request to the state's clemency board asking them to reconsidering pardoning Hill and commuting his sentence to life without parole.

This is a repeat of events last July when Hill came within 90 minutes of losing his life before the highest court in Georgia stepped in and ordered a stay.

The second petition is with the US supreme court and relates to its 2002 ruling, Atkins v Virginia, in which it decreed that putting to death a "mentally retarded" person was a violation of the eighth amendment of the US constitution that prohibits cruel and unusual punishment. The justices left it up to individual states to set their own definitions of "mental retardation", though they did specify that local procedures had to be "appropriate".

Kammer's petition to the supreme court focuses on the concept of "appropriate".

"That word indicates that states don't have unlimited latitude, they can't just do whatever they want."