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Andrea Yates' attorneys entered a plea of not guilty by reason of insanity at Wednesday's arraignment.

HOUSTON, Texas (CNN) -- The Harris County prosecutor Thursday defended his decision to seek the death penalty against Andrea Yates, the Texas mother accused of drowning her five children in the family bathtub.

In an interview with CNN, District Attorney Chuck Rosenthal said the question of what constitutes an appropriate punishment should rest with jurors.

"The jury in this case ought to have a lot of options, including the death penalty," Rosenthal said.

A gag order imposed by the judge prevented Rosenthal from talking about specifics in the case, but he said it has generated "more letters and e-mails" to his office than any other case in his 24-year career.

EXTRA INFORMATION In-depth: The case of Andrea Yates     VIDEO Andrea Yates is charged with murder stemming from the drowning deaths of her five children. CNN's Ed Lavandera reports (July 30) Play video (QuickTime, Real or Windows Media)   RESOURCES Message Board: Family violence

"Some of the e-mails basically accuse me of being barbaric ... and they wish all sorts of bad things on me and my family," he said. There have also been supportive e-mails, and Rosenthal said he is trying to respond to all of them.

The letters and e-mails, he said, have come from as far away as Australia, Europe and Asia.

Rosenthal said critics of his decision don't know the full story of what happened that morning in June when, police said, Yates systematically drowned her children, one by one.

Through her attorney, Yates has pleaded not guilty by reason of insanity to capital murder charges. Her attorney and family said she suffered from severe postpartum depression and remains in a psychotic state.

"A lot of the people who prejudge this case and who are sympathetic to the defendant don't know the facts," Rosenthal said.

Yates' legal team held a brief news conference Thursday to announce the formation of a fund to help pay for her legal defense. Defense attorney George Parnham said they could not say anything else about the case because of the gag order.

Andrea Yate's family and legal team react to the prosecution's decision to seek the death penalty.

Yates' husband, Russell Yates, said he could not discuss his feelings about the decision to seek the death penalty, but said "all of the evidence will eventually come out."

He said the deaths of his children was a "huge loss."

"They were my friends and I miss them every day." he said "It's hard, I see reminders of them everywhere I go now, not just at home, but in public."

Wednesday, at Yates' arraignment, a judge granted a defense request for a competency hearing for Yates.

In the next couple of weeks, a jury will hear from medical experts and determine whether Yates is fit to stand trial.

If a jury decides Yates is not competent, she will be sent to a state mental hospital until doctors determine she is competent.

CNN's Ed Lavandera contributed to this report