Cruz has admitted to the shooting, and has been charged with 17 counts of premeditated murder.
While the death penalty on the table may or may not bring relief to Cruz's victims and families of the deceased, the Washington Post points out that the decision made by prosecutors will likely result in a long, drawn-out trial which would include emotional testimony from Marjory Stoneman Douglas survivors, and what they witnessed that day.
Attorney Michael Satz filed the formal notice.
Cruz has another formal arraignment scheduled for Wednesday, during which he is expected to be arraigned on an additional 17 counts of first-degree murder.
The filing follows after Mr Cruz's attorneys signalled that their client was willing to plead guilty to avoid the death penalty.More news: ICE spokesperson quits over 'false public statements' from Trump administration
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If he does reach a plea deal with prosecutors, the only other option for Cruz is life in prison without the possibility of parole.
In an email Tuesday, Finkelstein said Cruz is "immediately ready" to plead guilty in return for 34 consecutive life sentences.
Cruz now "stands mute" to the charges against him.
His intestinal area has been sealed off and he is breathing on his own after being taken off a ventilator, family attorney Alex Arreaza said.
The shooting has sparked a fierce national debate over gun rights, with numerous student survivors vowing to push for gun control regulations so that the shooting they lived through might be the last.
Tony Montalto's daughter was one of 17 killed at Marjory Stoneman Douglas in February.