His previous not guilty plea indicated that Cruz denied his alleged role in the shooting, even though the evidence against him is overwhelming and Cruz himself has confessed to authorities, they say.
Satz formally submitted a notice of intent to seek death with the Clerk of Courts on Tuesday.
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Satz argued that the death penalty was warranted because Cruz "knowingly created a great risk of death to many persons" and committed a crime in a "cold, calculated and premeditated manner without any pretense of moral or legal justification", and because the crime "was especially heinous, atrocious or cruel", according to a copy of the filing.
Last week Cruz, above, appeared before magistrate court via video where 17 attempted murder charges were added by the grand jury to the existing premeditated murder charges.
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The only other penalty option for Cruz is life in prison with no possibility of parole.
"If not allowed to do that tomorrow (at the hearing), out of respect for the victims' families we will stand mute to the charges at the arraignment".
Cruz now "stands mute" before the charges, having withdrawn a written "not guilty" plea after being indicted by the grand jury. "We are not saying he is not guilty but we can't plead guilty while death is still on the table", Mr Finkelstein said.
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Daniel Reed, a parent of a student at Marjory Stoneman Douglas who initiated a petition drive seeking to have Amazon remove the National Rifle Association's channel from its offerings, said he was opposed to the death penalty for Cruz.