On Friday, prosecutors rejected an offer from James Holmes to plead guilty in order to avoid execution.
James Holmes, 25, is charged with multiple counts of murder and attempted murder in the attack in Aurora, one of the worst mass shootings in US history.
Dozens were wounded in the attack at a midnight showing of a Batman film.
“It’s my determination and my intention that in this case for James Eagan Holmes justice is death,” Arapahoe County District Attorney George Brauchler said at Monday’s hearing, which the accused attended.
James Holmes’ parents sat holding hands in the public gallery.
Victims and their families said they did not welcome the thought of a lengthy trial.
Pierce O’Farrill, who was shot three times in the attack, told the Associated Press: “All of us victims would be dragged along potentially for years. It could be 10 or 15 years before he’s executed.
“I would be in my 40s and I’m planning to have a family, and the thought of having to look back and reliving everything at that point in my life, it would be difficult.”
Last week, prosecutors argued that the defence motion for a guilty plea was not valid as a plea deal, but correspondents say such an agreement could still be reached before the case goes to trial.
James Holmes’ defence lawyers were expected to argue he is not guilty because he was legally insane at the time of the shooting on July 20.
But investigators say James Holmes, a former neuroscience graduate student, had stockpiled weapons and ammunition ahead of the attacks.
James Holmes allegedly also booby-trapped his flat to explode, in an apparent bid to distract police from responding to the cinema during the shooting.
In March, Colorado introduced new gun legislation to impose limits on the size of ammunition magazines and expand background checks for gun buyers.
The law bans the type of magazine used to fire dozens of bullets in just a few seconds during the Aurora shooting.
President Barack Obama is scheduled to visit Denver, Colorado, on Wednesday to highlight the bill as part of a campaign for national gun control measures in the wake of a mass shooting at an elementary school in December, in the state of Connecticut.
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