During a court hearing Tuesday, Fine rescinded his ruling, which he made last week in granting a pretrial motion in a capital murder case. But he asked Harris County prosecutors and defense attorneys to submit motions on the issue.
A hearing in the case is set for April 27, and Tuesday's decision will delay the trial, which had been set to begin with jury selection at the end of this month.
Fine said there was no precedent to guide him in resolving the issues raised by defense attorneys in a case involving a man accused of fatally shooting a Houston woman and wounding her sister during a robbery in front of their home in June 2008.
Attorneys for John Edward Green Jr. argued Texas' death penalty statute is unconstitutional because it violates their client's right to due process of law under the 5th Amendment because hundreds of innocent people around the country have been convicted and sent to death row and later exonerated.
Fine said in his ruling Thursday that it is safe to assume innocent people have been executed. A string of high-profile Texans, including Gov. Rick Perry, strongly criticized Fine's ruling last week. Fine declined to comment Tuesday on why he took back his ruling.
"We are reviewing the court's latest ruling and are briefing the issues," said Donna Hawkins, a spokeswoman for the Harris County District Attorney's Office.
An attorney for Green did not immediately return a telephone call seeking comment.
A court hearing in the case had been set for Wednesday, when Fine was expected to rule on prosecutors' motions to have him reconsider his decision or to still proceed with the trial as a death penalty case. Tuesday's hearing was called at the last minute.
Texas Attorney General Greg Abbott last week called Fine's ruling one of "unabashed judicial activism." Perry also slammed it, saying he supports the death penalty as do the majority of people in Texas.
Last year, the state executed 24 people, including six cases from Harris County. Three people have been executed so far this year, none from Harris County.