The Texas Supreme Court issued a last-minute stay of execution on Thursday to an autistic man whose murder conviction was based on what his lawyers say was a misdiagnosis of "shaken baby syndrome."

Robert Roberson, 57, had been scheduled to die by lethal injection at the state penitentiary in Huntsville on Thursday for the February 2002 death of his two-year-old daughter, Nikki.

But the Texas Supreme Court temporarily stayed the execution following an appeal from Texas lawmakers who issued a subpoena to Roberson so he can testify before a House committee that is examining his conviction.

"If the sentence is carried out, the witness obviously cannot appear," wrote Justice Evan Young.

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 committee has subpoenaed him to testify on Monday.

Roberson is one of two death row inmates who were to be executed in the United States on Thursday.

According to the Mayo Clinic, shaken baby syndrome is a serious brain injury resulting from forcefully shaking an infant or toddler.

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.

His legal efforts had been thwarted however until the Texas Supreme Court decision.

The Texas Board of Pardons and Paroles declined by a 6-0 vote to recommend clemency to Roberson and the US Supreme Court also rejected his request for a stay of execution, denying it without comment.

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.

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

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 20 executions in the United States this year including five in Alabama.