Houston, Texas - A planned appearance on Monday before the Texas legislature of an autistic man on death row convicted in a problematic "shaken baby" case has been postponed, lawmakers said.

Robert Roberson (57) had been scheduled to be put to death by lethal injection last week, but his execution was put on hold at the 11th hour after he was subpoenaed to testify before the Texas House Committee on Criminal Jurisprudence.

The office of the Texas attorney general objected to having Roberson appear in person, however, and committee members said his testimony has been postponed.

Representative Joe Moody, the committee chair, said he was "very disappointed" that Roberson would not appear before the committee on Monday, but lawmakers were in talks with the attorney general's office about having him show up at a later date.

"We didn't issue the subpoena to create a constitutional crisis, and we aren't interested in escalating a division between branches of government," Moody said.

He said a proposal had been made that Roberson testify by video conference.

"I believe that would be perfectly reasonable for most inmate witnesses," Moody said. "But Robert is a person with autism who has significant communication challenges."

Roberson 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 stayed his execution in response to the extraordinary bipartisan subpoena from lawmakers looking into his controversial conviction and the use of "junk science" in criminal prosecutions.

A bipartisan group of 86 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 of 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 attorney, Gretchen Sween, said new medical and scientific evidence 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, aggravated by doctors prescribing improper medication, Sween said.

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

Roberson's legal efforts to save his life had been thwarted at every turn until the Texas Supreme Court stepped in, granting him a temporary reprieve.

Texas Governor Greg Abbott has asked the state supreme court to dismiss the subpoena from the state legislature.

"Unless the Court rejects that tactic, it can be repeated in every capital case, effectively rewriting the Constitution to reassign a power given only to the Governor," Abbott said.

"The power to grant clemency in a capital case, including a 30-day reprieve, is vested in the Governor alone," he said.