Washington DC - The US Supreme Court on Thursday denied a stay of execution for an autistic man convicted of murder in a "shaken baby syndrome" case – although his lawyers managed to secure a potential last-minute delay from a judge in Texas.

Robert Roberson (57) was scheduled to die by lethal injection at the state penitentiary in Huntsville at 6:00 PM Central Time for the February 2002 death of his 2-year-old daughter, Nikki.

The conservative-majority Supreme Court denied Roberson's request for a stay of execution without comment.

But a district court judge in Texas issued a temporary order that would delay Roberson's execution so he could respond to a subpoena issued by a Texas House of Representatives committee that is examining his conviction.

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Texas Attorney General Ken Paxton filed an appeal seeking a lifting of the temporary order and it was not immediately clear if it would be granted, allowing the execution to proceed.

A bipartisan group of 86 Texas lawmakers has urged clemency for Roberson, citing "voluminous new scientific evidence" that casts doubt on his guilt, and the House committee has subpoenaed him to testify on Monday.

Roberson has maintained his innocence and his attorney, Gretchen Sween, said there is "overwhelming new medical and scientific evidence" that shows his daughter died of "natural and accidental causes, not abuse."

The diagnosis of shaken baby syndrome, made at the hospital where Roberson's chronically ill daughter died, was erroneous and the cause of death was in fact pneumonia which was aggravated when doctors prescribed improper medication, Sween said.

The Texas Board of Pardons and Paroles declined by a 6-0 vote on Wednesday to recommend clemency to Roberson and commute his sentence to life in prison.

Texas Governor Greg Abbott is unable to grant clemency without a recommendation from the board, but he can grant a 30-day reprieve of Roberson's death sentence.

Roberson's case has drawn the attention of the Innocence Project, which works to reverse wrongful convictions, as well as best-selling American novelist John Grisham, Texas lawmakers, and medical experts.

Also among those seeking to halt his execution is the man who put him behind bars – Brian Wharton, the former chief detective in the town of Palestine.

"Knowing everything that I know now, I am firmly convinced that Robert is an innocent man," Wharton said at a recent press conference organized by Roberson's supporters.

Grisham, author of the legal thrillers The Firm and A Time to Kill, also appeared at the event and said, "What's amazing about Robert's case is that there was no crime."

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Roberson would be the first person executed in the US based on a conviction of shaken baby syndrome, according to his lawyers.

Kate Judson of the Center for Integrity in Forensic Sciences said more than 30 parents and caregivers in 18 US states have been exonerated after being wrongfully convicted using "unscientific" shaken baby testimony.

Sween said Roberson's autism spectrum disorder, which was not diagnosed until 2018, contributed to his arrest and conviction.

"It is quite possible that Mr Roberson would not be on death row today, but for his autism," she said.

Sween said staff at the hospital where his daughter was admitted did not know he had autism and "judged his flat affect as a sign of guilt."

There have been 19 executions in the US this year.