A Texas court has halted the execution of a man convicted of killing his two-year-old daughter in a "shaken baby syndrome" case.

Death row inmate Robert Roberson, who has always maintained the child died from complications linked to pneumonia, had been scheduled for execution on 16 October.

The diagnosis of shaken baby syndrome refers to a serious brain injury resulting from forcefully shaking an infant or a toddler.

On Thursday, the Texas Court of Criminal Appeals granted an emergency stay under the state's 2013 "junk science" law that allows courts to re-examine convictions based on scientific evidence that has since been debunked or evolved.

In recent years, lawmakers from both major parties have urged a re-examination of the case, which Roberson's lawyers say was built on outdated medical theories.