Houston, Texas - A Texas appeals court on Thursday halted the scheduled execution of an autistic man convicted in a problematic "shaken baby" case.

Robert Roberson (58) had been scheduled to be put to death by lethal injection next week for the 2002 death of his two-year-old daughter, Nikki.

The Texas Court of Criminal Appeals granted a stay of execution to Roberson so a lower court can consider a challenge to his conviction and the evidence of shaken baby syndrome.

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A bipartisan group of Texas lawmakers has urged clemency for Roberson, citing "voluminous new scientific evidence" that casts doubt on his guilt.

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

His case has drawn the attention of not only Texas lawmakers but also best-selling American novelist John Grisham, medical experts, and the Innocence Project, which works to reverse wrongful convictions.

Also among his supporters is the man who put him behind bars – Brian Wharton, the former chief detective in the town of Palestine – who has said "knowing everything that I know now, I am firmly convinced that Robert is an innocent man."

Roberson has always maintained his innocence, and his lawyers maintain his chronically ill daughter died of natural and accidental causes, not abuse.

The diagnosis of shaken baby syndrome, made at the hospital where Roberson's daughter died, was erroneous, they say, and the cause of death was pneumonia, aggravated by doctors prescribing improper medication.

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

There have been 34 executions in the US this year.